EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 July 2021 Shift 2>Q 7

MEDIUM

JEE Main

IMPORTANT

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Consider function $f : A \to B$ and $g : B \to C (A, B, C \subseteq R)$ such that ${(g o f)}^{- 1}$ exists, then:

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Important Questions on Functions

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 27 July 2021 Shift 1>Q 8

Let

S = \{1, 2, 3, 4, 5, 6, 7\} .

Then the number of possible functions

f : S \to S

such that

f (m \cdot n) = f (m) \cdot f (n)

for every

m, n \in S

and

m \cdot n \in S

, is equal to _____.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 27 July 2021 Shift 2>Q 9

Let

f : R \to R

be defined as

f (x + y) + f (x - y) = 2 f (x) f (y), f (\frac{1}{2}) = - 1 .

Then the value of

\sum_{k = 1}^{20} \frac{1}{\sin (k) \sin (k + f (k))}

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 16 March 2021 Shift 2>Q 10

Let

f : R \to R

and

g : R \to R

be defined as

f (x) = \{\begin{array}{cl} x + a, & x < 0 \\ | x - 1 |, & x \geq 0 \end{array}

and

g (x) = \{\begin{matrix} x + 1, & x < 0 \\ (x - 1)^{2} + b, & x \geq 0 \end{matrix}

, where

a, b

are non-negative real numbers. If

g o f (x)

is continuous for all

x \in R,

then

a + b

is equal to ______ .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 17 March 2021 Shift 1>Q 11

The inverse of

y = 5^{\log x}

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 17 March 2021 Shift 2>Q 12

Let

f : [- 1, 1] \to R

be defined as

f (x) = a x^{2} + b x + c

for all

x \in [- 1, 1],

where

a, b, c \in R

such that

f (- 1) = 2, f^{'} (- 1) = 1

and for

x \in (- 1, 1)

the maximum value of

f^{"} (x)

is

\frac{1}{2} .

If

f (x) \leq α, x \in [- 1, 1],

then the least value of

α

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 18 March 2021 Shift 1>Q 13

The real valued function $f (x) = \frac{{cosec}^{- 1} x}{\sqrt{x - [x]}},$ where $[x]$ denotes the greatest integer less than or equal to $x,$ is defined for all $x$ belonging to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 18 March 2021 Shift 1>Q 14

If the functions are defined as

f (x) = \sqrt{x}

and

g (x) = \sqrt{1 - x},

then what is the common domain of the following functions:

f + g, f - g, f / g, g / f, g - f

, where

(f \pm g) (x) = f (x) \pm g (x), (f / g) (x) = \frac{f (x)}{g (x)}

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 18 March 2021 Shift 2>Q 15

Let

f : R - {3} \to R - {1}

be defined by

f (x) = \frac{x - 2}{x - 3}

. Let

g : R \to R

be given as

g (x) = 2 x - 3

. Then, the sum of all the values of

x

for which

f^{- 1} (x) + g^{- 1} (x) = \frac{13}{2}

is equal to