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

EASY

JEE Main

IMPORTANT

Earn 100

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:

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Important Questions on Functions

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

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main 18 March 2021 Shift 2>Q 16

If

f (x)

and

g (x)

are two polynomials such that the polynomial

P (x) = f (x^{3}) + x g (x^{3})

is divisible by

x^{2} + x + 1

, then

P (1)

is equal to ___ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 24 Feb 2021 Shift 1>Q 17

Let

f : R \to R

be defined as

f (x) = 2 x - 1

and

g : R - \{1\} \to R

. be defined as

g (x) = \frac{x - \frac{1}{2}}{x - 1}

. Then the composition function

f (g (x))

is:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 24 Feb 2021 Shift 2>Q 18

If

a + α = 1, b + β = 2

and

a f (x) + α f (\frac{1}{x}) = b x + \frac{β}{x}, x \neq 0,

then the value of the expression

\frac{f (x) + f (\frac{1}{x})}{x + \frac{1}{x}}

is ___________.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 Feb 2021 Shift 1>Q 19

Let

f, g : N \to N

such that

f (n + 1) = f (n) + f (1) \forall n \in N

and

g

be any arbitrary function. Which of the following statements is NOT true?

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 25 Feb 2021 Shift 2>Q 20

A function $f (x)$ is given by $f (x) = \frac{5^{x}}{5^{x} + 5}$ , then the sum of the series $f (\frac{1}{20}) + f (\frac{2}{20}) + f (\frac{3}{20}) + \dots + f (\frac{39}{20})$ is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 23 - Functions>JEE Main - 26 Feb 2021 Shift 1>Q 21

The number of solutions of the equation

\log_{4} (x - 1) = \log_{2} (x - 3)

is ______.