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

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

$g (y) = 4 + \frac{y + 3}{4}$
$g (y) = \frac{y + 3}{4}$
$g (y) = \frac{y - 3}{4}$
$g (y) = \frac{3 y + 4}{4}$

The correct answer is: $g left parenthesis y right parenthesis equals fraction numerator y minus 3 over denominator 4 end fraction$

$g left parenthesis y right parenthesis equals x not stretchy rightwards double arrow f to the power of negative 1 end exponent left parenthesis y right parenthesis equals x not stretchy rightwards double arrow f left parenthesis x right parenthesis equals y not stretchy rightwards double arrow 4 x plus 3 equals y not stretchy rightwards double arrow 4 x equals y minus 3 not stretchy rightwards double arrow x equals left parenthesis y minus 3 right parenthesis divided by 4 not stretchy rightwards double arrow g left parenthesis y right parenthesis equals left parenthesis y minus 3 right parenthesis divided by 4$

Related Questions to study

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

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

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

MathematicsFunctions

parallel

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

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

parallel

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

$text If end text f colon R not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction straight for all x element of R text end text$ is surjective then A =

$text If end text f colon R not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction straight for all x element of R text end text$ is surjective then A =

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator a to the power of x minus 1 over denominator x to the power of n open parentheses a to the power of x plus 1 close parentheses end fraction$ is even then n =

$text If end text f left parenthesis x right parenthesis equals fraction numerator a to the power of x minus 1 over denominator x to the power of n open parentheses a to the power of x plus 1 close parentheses end fraction$ is even then n =

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

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

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

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

$text Let end text g colon R not stretchy rightwards arrow open parentheses 0 comma pi over 3 close square brackets text be defined by end text g left parenthesis x right parenthesis equals cos to the power of negative 1 end exponent open parentheses fraction numerator x squared minus k over denominator 1 plus x squared end fraction close parentheses space$ Then find the possible values of k for which g is surjective function

$text Let end text g colon R not stretchy rightwards arrow open parentheses 0 comma pi over 3 close square brackets text be defined by end text g left parenthesis x right parenthesis equals cos to the power of negative 1 end exponent open parentheses fraction numerator x squared minus k over denominator 1 plus x squared end fraction close parentheses space$ Then find the possible values of k for which g is surjective function

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.