EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2020 (Sep-23 Shift-1)>Q 5

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IMPORTANT

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If $f : R \to R$ is defined as $f (x) = x - [x] + 3, \forall x \in R,$ then $f$ is (where, $[\cdot]$ is GIF)

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Important Questions on Functions

HARD

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2018 (25-APR Shift-1)>Q 6

If

f : ℝ \to ℝ

is such that

f (x + y) = f (x) + f (y)

for all

x, y \in ℝ, f (1) = 7

and

\sum_{r = 1}^{n} f (r) = 14112,

then

MEDIUM

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Afternoon>Q 7

If

f (10 - x) = 3 x^{2} + 4 x - 5

and

f (x) = p x^{2} + q x + r

then

p + q + r =

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2020 (Sep-23 Shift-1)>Q 8

If

f

is a continuous real-valued function, then the range of the function is _______

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2021 (19-Aug Forenoon)>Q 9

Given the function

f (x) = \frac{a^{x} + a^{- x}}{2}, (a > 2)

then

f (x + y) + f (x - y)

is equal to

MEDIUM

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET 2021 (19-Aug Afternoon)>Q 10

Let

f : R \to R

be a function defined by

f (x) = \frac{4^{x}}{4^{x} + 2}

. what is the value of

f (\frac{1}{4}) + 2 f (\frac{1}{2}) + f (\frac{3}{4}) =

?

EASY

AP EAPCET

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 18 - Functions>AP EAPCET - 20 Aug 2021 Forenoon>Q 11

If

f : z \to z

is defined by

f (x) = x^{9} - 11 x^{8} - 2 x^{7} + 22 x^{6} + x^{4} - 12 x^{3} + 11 x^{2} + x - 3 \forall x \in z

, then

f (11) =

MEDIUM

AP EAPCET

IMPORTANT

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

The real valued function

f (x) = \frac{x}{e^{x} - 1} + \frac{x}{2} + 1

defined on

R \ {0}

is

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