EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2021 (19-Aug Afternoon)>Q 12

MEDIUM

AP EAPCET

IMPORTANT

Earn 100

The real valued function $f (x) = \frac{x}{e^{x} - 1} + \frac{x}{2} + 1$ defined on $R \ {0}$ is

50% studentsanswered this correctly

Important Questions on Functions

MEDIUM

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2019 (21-Apr Shift-2)>Q 13

Let

A

and

B

be finite sets and

P_{A}

and

P_{B}

, respectively denote their power sets. If

P_{B}

has

112

elements more than those in

P_{A}

, then the number of functions from

A

to

B

which are injective is

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2020 (Sep-23 Shift-1)>Q 14

If

f : R \to R

is defined as

f (x) = {(2020 - x^{2019})}^{1 / 2019}, \forall x \in R,

find

(f \circ f \circ f \circ f) (\frac{2019}{2020})

MEDIUM

AP EAPCET

IMPORTANT

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

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?

EASY

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 $(g o f) (x) =$

EASY

AP EAPCET

IMPORTANT

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)

MEDIUM

AP EAPCET

IMPORTANT

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

AP EAPCET

IMPORTANT

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

AP EAPCET

IMPORTANT

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