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

The range of $fraction numerator x squared minus 4 over denominator x minus 2 end fraction text is end text$

$R$
$R - {2}$
$R - {\pm 2}$
$R - {4}$

The correct answer is: $R minus left curly bracket 4 right curly bracket$

$text Clearly the range of end text x plus 2 text is end text R. x not equal to 2 not stretchy rightwards double arrow x plus 2 not equal to 4 not stretchy rightwards double arrow fraction numerator left parenthesis x plus 2 right parenthesis left parenthesis x minus 2 right parenthesis over denominator x minus 2 end fraction not equal to 4 not stretchy rightwards double arrow fraction numerator x squared minus 4 over denominator x minus 2 end fraction not equal to 4 therefore text Range end text equals R minus left curly bracket 4 right curly bracket$

Related Questions to study

The range of $sec squared x plus 4 cosec squared x$ is

The range of $sec squared x plus 4 cosec squared x$ is

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals a x to the power of 7 plus b x cubed plus c x minus 5 text and end text f left parenthesis negative 7 right parenthesis equals 7$ , then the range of $f left parenthesis 7 right parenthesis plus 17 cos x text is end text$

$text If end text f left parenthesis x right parenthesis equals a x to the power of 7 plus b x cubed plus c x minus 5 text and end text f left parenthesis negative 7 right parenthesis equals 7$ , then the range of $f left parenthesis 7 right parenthesis plus 17 cos x text is end text$

MathematicsFunctions

Domain of $text end text f left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent x plus Sec to the power of negative 1 end exponent x text is end text$

Domain of $text end text f left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent x plus Sec to the power of negative 1 end exponent x text is end text$

MathematicsFunctions

parallel

The domain of the function $f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript open parentheses x squared minus 1 close parentheses text is end text$

The domain of the function $f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript open parentheses x squared minus 1 close parentheses text is end text$

MathematicsFunctions

The domain of $text end text f left parenthesis x right parenthesis equals open parentheses fraction numerator 1 over denominator vertical line x vertical line minus 1 end fraction close parentheses to the power of 1 over 2006 end exponent text is end text$

The domain of $text end text f left parenthesis x right parenthesis equals open parentheses fraction numerator 1 over denominator vertical line x vertical line minus 1 end fraction close parentheses to the power of 1 over 2006 end exponent text is end text$

MathematicsFunctions

The domain of the function f(x) =

The domain of the function f(x) =

MathematicsFunctions

parallel

The domain of $square root of left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end root text is end text$

The domain of $square root of left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end root text is end text$

MathematicsFunctions

The domain of the function f(x) = $fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text is : end text$

The domain of the function f(x) = $fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text is : end text$

MathematicsFunctions

$text If end text f colon R rightwards arrow R text and end text g colon R rightwards arrow R text are defined by end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket text and end text g left parenthesis x right parenthesis equals left square bracket x right square bracket text for end text x element of R text , end text$ where [x] is the greatest integer not exceeding x, $text then for every end text x element of R comma f left parenthesis g left parenthesis x right parenthesis right parenthesis equals$

$text If end text f colon R rightwards arrow R text and end text g colon R rightwards arrow R text are defined by end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket text and end text g left parenthesis x right parenthesis equals left square bracket x right square bracket text for end text x element of R text , end text$ where [x] is the greatest integer not exceeding x, $text then for every end text x element of R comma f left parenthesis g left parenthesis x right parenthesis right parenthesis equals$

MathematicsFunctions

parallel

$text If end text f left parenthesis x right parenthesis equals left square bracket x right square bracket comma space g left parenthesis x right parenthesis equals x minus left square bracket x right square bracket$ Then which of the following functions is the zero functions

$text If end text f left parenthesis x right parenthesis equals left square bracket x right square bracket comma space g left parenthesis x right parenthesis equals x minus left square bracket x right square bracket$ Then which of the following functions is the zero functions

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 minus x squared end root end fraction comma space g left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 plus x squared end root end fraction text then end text left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals$

$text If end text f left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 minus x squared end root end fraction comma space g left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 plus x squared end root end fraction text then end text left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals$

MathematicsFunctions

$text For end text x element of R minus left curly bracket 0 comma 1 right curly bracket comma less or equal than t f subscript 1 left parenthesis x right parenthesis equals 1 over x comma f subscript 2 left parenthesis x right parenthesis equals 1 minus x text and end text f subscript 3 left parenthesis x right parenthesis equals fraction numerator 1 over denominator 1 minus x end fraction$ be three given functions if a function,j(x) satisfies $open parentheses f subscript 2 ring operator J ring operator f subscript 1 close parentheses left parenthesis x right parenthesis equals f subscript 3 left parenthesis x right parenthesis comma then J left parenthesis x right parenthesis$ is equal to

$text For end text x element of R minus left curly bracket 0 comma 1 right curly bracket comma less or equal than t f subscript 1 left parenthesis x right parenthesis equals 1 over x comma f subscript 2 left parenthesis x right parenthesis equals 1 minus x text and end text f subscript 3 left parenthesis x right parenthesis equals fraction numerator 1 over denominator 1 minus x end fraction$ be three given functions if a function,j(x) satisfies $open parentheses f subscript 2 ring operator J ring operator f subscript 1 close parentheses left parenthesis x right parenthesis equals f subscript 3 left parenthesis x right parenthesis comma then J left parenthesis x right parenthesis$ is equal to

MathematicsFunctions

parallel

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

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

MathematicsFunctions

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

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

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

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.