Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Mathematics

Functions

Easy

Question

$text If end text f left parenthesis x right parenthesis equals sin squared x plus sin squared left parenthesis x plus pi divided by 3 right parenthesis plus cos x cos left parenthesis x plus pi divided by 3 right parenthesis space a n d space g left parenthesis 5 divided by 4 right parenthesis equals 1 text then end text open parentheses g o f close parentheses left parenthesis x right parenthesis equals$

$1$
$0$
$\sin x$
$none$

The correct answer is: $1$

$f left parenthesis x right parenthesis equals sin squared x plus left parenthesis sin x cos pi divided by 3 plus cos x sin pi divided by 3 right parenthesis squared plus cos x left parenthesis cos x cos pi divided by 3 minus sin x sin pi divided by 3 right parenthesis equals sin squared x plus open parentheses fraction numerator sin x over denominator 2 end fraction plus fraction numerator square root of 3 cos x over denominator 2 end fraction close parentheses squared plus fraction numerator cos squared x over denominator 2 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction cos x sin x equals sin squared x plus fraction numerator sin squared x over denominator 4 end fraction plus 3 over 4 cos squared x plus fraction numerator square root of 3 over denominator 2 end fraction sin x cos x plus fraction numerator cos squared x over denominator 2 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction cos x sin x equals 5 over 4 open parentheses sin squared x plus cos squared x close parentheses equals 5 over 4 therefore left square bracket g ring operator f right square bracket left parenthesis x right parenthesis equals g left square bracket f left parenthesis x right parenthesis right square bracket equals g left parenthesis 5 divided by 4 right parenthesis equals 1$

Related Questions to study

$text If end text f colon left square bracket negative 6 comma 6 right square bracket not stretchy rightwards arrow R text is defined by end text f left parenthesis x right parenthesis equals x squared minus 3 text for end text x element of R text then end text open parentheses f space o space f space o space f close parentheses left parenthesis negative 1 right parenthesis plus open parentheses f space o space f space o space f close parentheses left parenthesis 0 right parenthesis plus open parentheses f space o space f space o space f close parentheses left parenthesis 1 right parenthesis equals$

$text If end text f colon left square bracket negative 6 comma 6 right square bracket not stretchy rightwards arrow R text is defined by end text f left parenthesis x right parenthesis equals x squared minus 3 text for end text x element of R text then end text open parentheses f space o space f space o space f close parentheses left parenthesis negative 1 right parenthesis plus open parentheses f space o space f space o space f close parentheses left parenthesis 0 right parenthesis plus open parentheses f space o space f space o space f close parentheses left parenthesis 1 right parenthesis equals$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals open parentheses a minus x to the power of n close parentheses to the power of 1 divided by n end exponent comma text where end text a greater than 0 text and end text n element of N comma text then end text open parentheses f subscript 0 f close parentheses left parenthesis x right parenthesis equals$

$text If end text f left parenthesis x right parenthesis equals open parentheses a minus x to the power of n close parentheses to the power of 1 divided by n end exponent comma text where end text a greater than 0 text and end text n element of N comma text then end text open parentheses f subscript 0 f close parentheses left parenthesis x right parenthesis equals$

MathematicsFunctions

$text If end text F left parenthesis n right parenthesis equals left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent left parenthesis n minus 1 right parenthesis text and G end text left parenthesis n right parenthesis equals n minus F left parenthesis n right parenthesis space straight for all n element of N text then end text open parentheses G subscript 0 G close parentheses left parenthesis n right parenthesis equals$

$text If end text F left parenthesis n right parenthesis equals left parenthesis negative 1 right parenthesis to the power of n minus 1 end exponent left parenthesis n minus 1 right parenthesis text and G end text left parenthesis n right parenthesis equals n minus F left parenthesis n right parenthesis space straight for all n element of N text then end text open parentheses G subscript 0 G close parentheses left parenthesis n right parenthesis equals$

MathematicsFunctions

parallel

$text If end text g left square bracket f left parenthesis x right parenthesis right square bracket equals vertical line sin x vertical line comma space f left square bracket g left parenthesis x right parenthesis right square bracket equals left parenthesis sin square root of x right parenthesis squared text then end text$

$text If end text g left square bracket f left parenthesis x right parenthesis right square bracket equals vertical line sin x vertical line comma space f left square bracket g left parenthesis x right parenthesis right square bracket equals left parenthesis sin square root of x right parenthesis squared text then end text$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared minus 1 comma x greater or equal than negative 1 text then the set end text S equals open curly brackets x element of R colon f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent x close curly brackets text is end text$

$text If end text f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared minus 1 comma x greater or equal than negative 1 text then the set end text S equals open curly brackets x element of R colon f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent x close curly brackets text is end text$

MathematicsFunctions

$text Let end text x not equal to 0 comma vertical line x vertical line less than 1 half text and end text f left parenthesis x right parenthesis equals 1 plus 2 x plus 4 x squared plus 8 x cubed plus horizontal ellipsis. text Then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

$text Let end text x not equal to 0 comma vertical line x vertical line less than 1 half text and end text f left parenthesis x right parenthesis equals 1 plus 2 x plus 4 x squared plus 8 x cubed plus horizontal ellipsis. text Then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

MathematicsFunctions

parallel

$text If end text f colon left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 1 comma straight infinity right square bracket text is defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 plus square root of 1 plus 4 log subscript 2 x end root over denominator 2 end fraction text then end text f to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals$

$text If end text f colon left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 1 comma straight infinity right square bracket text is defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 plus square root of 1 plus 4 log subscript 2 x end root over denominator 2 end fraction text then end text f to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals$

MathematicsFunctions

$text If end text f left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 1 comma straight infinity right parenthesis text is defined by end text f left parenthesis x right parenthesis equals 2 to the power of x left parenthesis x minus 1 right parenthesis end exponent text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

$text If end text f left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 1 comma straight infinity right parenthesis text is defined by end text f left parenthesis x right parenthesis equals 2 to the power of x left parenthesis x minus 1 right parenthesis end exponent text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

MathematicsFunctions

$text If end text f colon left curly bracket 1 comma 2 comma 3 comma midline horizontal ellipsis right curly bracket not stretchy rightwards arrow left curly bracket 0 comma plus-or-minus 1 comma plus-or-minus 2 comma midline horizontal ellipsis right curly bracket text is defined by end text f left parenthesis n right parenthesis equals open curly brackets table attributes columnalign center left columnspacing 1em rowspacing 4 pt end attributes row cell n divided by 2 end cell cell text if end text n text is even end text end cell row cell negative open parentheses fraction numerator n minus 1 over denominator 2 end fraction close parentheses end cell cell text if end text n text is odd end text end cell end table close t h e n space f to the power of negative 1 end exponent left parenthesis negative 100 right parenthesis space text is end text$

$text If end text f colon left curly bracket 1 comma 2 comma 3 comma midline horizontal ellipsis right curly bracket not stretchy rightwards arrow left curly bracket 0 comma plus-or-minus 1 comma plus-or-minus 2 comma midline horizontal ellipsis right curly bracket text is defined by end text f left parenthesis n right parenthesis equals open curly brackets table attributes columnalign center left columnspacing 1em rowspacing 4 pt end attributes row cell n divided by 2 end cell cell text if end text n text is even end text end cell row cell negative open parentheses fraction numerator n minus 1 over denominator 2 end fraction close parentheses end cell cell text if end text n text is odd end text end cell end table close t h e n space f to the power of negative 1 end exponent left parenthesis negative 100 right parenthesis space text is end text$

MathematicsFunctions

parallel

If [ ] denotes the greatest integer function and if $f colon left parenthesis 5 comma 10 right parenthesis rightwards arrow left parenthesis 7 comma 12 right parenthesis$ is a function defined by $f left parenthesis x right parenthesis equals x plus 2 open square brackets x over 5 close square brackets text , then end text$

If [ ] denotes the greatest integer function and if $f colon left parenthesis 5 comma 10 right parenthesis rightwards arrow left parenthesis 7 comma 12 right parenthesis$ is a function defined by $f left parenthesis x right parenthesis equals x plus 2 open square brackets x over 5 close square brackets text , then end text$

MathematicsFunctions

$text If end text f colon left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 2 comma straight infinity right parenthesis text is given by end text f left parenthesis x right parenthesis equals x plus 1 over x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

$text If end text f colon left square bracket 1 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 2 comma straight infinity right parenthesis text is given by end text f left parenthesis x right parenthesis equals x plus 1 over x text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

MathematicsFunctions

$text If end text f colon R minus left curly bracket 5 divided by 2 right curly bracket not stretchy rightwards arrow R minus left curly bracket negative 1 right curly bracket text is defined by end text f left parenthesis x right parenthesis equals fraction numerator 2 x plus 3 over denominator 5 minus 2 x end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

$text If end text f colon R minus left curly bracket 5 divided by 2 right curly bracket not stretchy rightwards arrow R minus left curly bracket negative 1 right curly bracket text is defined by end text f left parenthesis x right parenthesis equals fraction numerator 2 x plus 3 over denominator 5 minus 2 x end fraction text then end text f to the power of negative 1 end exponent left parenthesis x right parenthesis equals$

MathematicsFunctions

parallel

$text Let end text f colon N not stretchy rightwards arrow Y text be a function defined as end text f left parenthesis x right parenthesis equals 4 x plus 3 text where end text Y equals left curly bracket y element of N colon y equals 4 x plus 3 text for some end text x element of N right curly bracket.$
Inverse of f is ?

$text Let end text f colon N not stretchy rightwards arrow Y text be a function defined as end text f left parenthesis x right parenthesis equals 4 x plus 3 text where end text Y equals left curly bracket y element of N colon y equals 4 x plus 3 text for some end text x element of N right curly bracket.$
Inverse of f is ?

MathematicsFunctions

$f colon left square bracket negative 3 comma 3 right square bracket not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x cubed plus sin x plus open square brackets fraction numerator x squared plus 2 over denominator a end fraction close square brackets space text be an odd function when end text left square bracket times right square bracket text end text$
denotes greatest integer function then a is

$f colon left square bracket negative 3 comma 3 right square bracket not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x cubed plus sin x plus open square brackets fraction numerator x squared plus 2 over denominator a end fraction close square brackets space text be an odd function when end text left square bracket times right square bracket text end text$
denotes greatest integer function then a is

MathematicsFunctions

Among the following functions defined on R into R, the constant function is

Among the following functions defined on R into R, the constant function is

MathematicsFunctions

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.