EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2018 (25-APR Shift-1)>Q 15

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If $f : A \to B$ and $g : B \to C$ are two functions such that $g o f : A \to C$ is a bijection, then which one of the following is always true?

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Important Questions on Functions

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AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2021 (19-Aug Forenoon)>Q 16

Let $f : R \to R$ and $g : R \to R$ be defined by $f (x) = 2 x + 1 & g (x) = x^{2} - 2$ determine $(g o f) (x) =$

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2021 (19-Aug Forenoon)>Q 17

If

f

is a function defined on

(0, 1)

by

f (x) = \max {x - [x], - x - [x]}

, then

(f o f o f o f) (x)

is equal to ([.] greatest integer function)

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Forenoon>Q 18

f (x) = \sin x + \cos x, g (x) = x^{2} - 1

then

g (f (x))

is invertible if

EASY

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Forenoon>Q 19

Let

f (x) = x^{3}

and

g (x) = 3^{x}

, then the quadratic equation whose roots are solutions of the equation

(f \circ g) (x) = (g \circ f) (x) (

for

x \neq 0)

is

EASY

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Afternoon>Q 20

If

{}^{'}f^{'}

is the greatest integers function defined on

R

as

f (x) = [x]

and

{}^{'}g^{'}

is the modulus function defined on

R

as

g (x) = |x|

, then the value of

(g o f) (\frac{- 5}{3})

is

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AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Afternoon>Q 21

Let

f (x) = {(x + 2)}^{2} - 2, x \geq - 2

. Then

f^{- 1} (x) =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Afternoon>Q 22

If

f : R \to R

and

g : R \to R

are two functions defined by

f (x) = a x + b (a \neq 0) \forall x \in R

and

g (x) = c x^{3} + d (c \neq 0) \forall x \in R

, then

{(f o g)}^{- 1} (x) =