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

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

$\{0, - 1, \frac{- 3 + i \sqrt{3}}{2}, \frac{- 3 - i \sqrt{3}}{2}\}$
${0, 1, - 1}$
${0, - 1}$
$\emptyset$

The correct answer is: $left curly bracket 0 comma negative 1 right curly bracket$

$f to the power of negative 1 end exponent left parenthesis x right parenthesis equals y not stretchy rightwards double arrow x equals f left parenthesis y right parenthesis not stretchy rightwards double arrow x equals left parenthesis y plus 1 right parenthesis squared minus 1 not stretchy rightwards double arrow x plus 1 equals left parenthesis y plus 1 right parenthesis squared not stretchy rightwards double arrow y plus 1 equals square root of x plus 1 end root not stretchy rightwards double arrow y equals square root of x plus 1 end root minus 1 not stretchy rightwards double arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis equals square root of x plus 1 end root minus 1 f left parenthesis x right parenthesis equals f to the power of negative 1 end exponent left parenthesis x right parenthesis not stretchy rightwards double arrow left parenthesis x plus 1 right parenthesis squared minus 1 equals square root of x plus 1 end root minus 1 not stretchy rightwards double arrow left parenthesis x plus 1 right parenthesis squared equals square root of x plus 1 end root not stretchy rightwards double arrow left parenthesis x plus 1 right parenthesis to the power of 4 equals x plus 1 not stretchy rightwards double arrow x plus 1 equals 0 text or end text left parenthesis x plus 1 right parenthesis cubed equals 1 not stretchy rightwards double arrow x equals negative 1 text or end text x plus 1 equals 1 text or end text omega text or end text omega squared open square brackets text But end text omega comma omega squared text are imaginary end text close square brackets not stretchy rightwards double arrow x equals negative 1 text or end text x equals 0 therefore S equals left curly bracket 0 comma negative 1 right curly bracket$

Related Questions to study

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

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

MathematicsFunctions

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

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

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

parallel

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

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

MathematicsFunctions

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

parallel

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

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

MathematicsFunctions

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

parallel

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

$text Let end text f left parenthesis x right parenthesis equals fraction numerator x over denominator e to the power of x minus 1 end fraction plus x over 2 plus 1 comma text then end text f text is end text$

$text Let end text f left parenthesis x right parenthesis equals fraction numerator x over denominator e to the power of x minus 1 end fraction plus x over 2 plus 1 comma text then end text f text is end text$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator 2 x left parenthesis sin x plus tan x right parenthesis over denominator 2 open square brackets fraction numerator x plus 21 pi over denominator pi end fraction close square brackets minus 41 end fraction comma x not equal to n pi comma text end text$ then f is

$text If end text f left parenthesis x right parenthesis equals fraction numerator 2 x left parenthesis sin x plus tan x right parenthesis over denominator 2 open square brackets fraction numerator x plus 21 pi over denominator pi end fraction close square brackets minus 41 end fraction comma x not equal to n pi comma text end text$ then f is

MathematicsFunctions

parallel

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos x sin x over denominator tan x plus cot x end fraction$ then function f(x)

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos x sin x over denominator tan x plus cot x end fraction$ then function f(x)

MathematicsFunctions

The function $text end text f left parenthesis x right parenthesis equals log open parentheses x plus square root of x squared plus 1 end root close parentheses text is end text$

The function $text end text f left parenthesis x right parenthesis equals log open parentheses x plus square root of x squared plus 1 end root close parentheses text is end text$

MathematicsFunctions

$text If the function end text f colon R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator x squared over denominator 1 minus x squared end fraction comma text end text$ is surjective then A =

$text If the function end text f colon R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator x squared over denominator 1 minus x squared end fraction comma text end text$ is surjective then A =

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.