Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 25

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JEE Advanced

IMPORTANT

Earn 100

Two functions $f$ and $g$ are said to commute, if $(f o g) (x) = (g o f) (x), \forall x$ , then which one of the following functions are commute?

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Important Questions on Fundamentals of Relation and Function

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 26

If

f (x) = x^{2} + 1

, then the value of

(f o f) (x)

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 27

If

f (x)

is defined on

[0, 1]

by the rule

f (x) = \{\begin{array}{cl} x, & if x \in Q \\ 1 - x, & if x \notin Q \end{array}

, then for

x \in [0, 1]

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 28

If

f (x) = \{\begin{array}{l} x^{3} + 1, & x < 0 \\ x^{2} + 1, & x \geq 0 \end{array}, g (x) = \{\begin{cases} {(x - 1)}^{1 / 3}, & x < 1 \\ {(x - 1)}^{1 / 2}, & x \geq 1 \end{cases}

, then

(g o f) (x)

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 29

If

f (x) = [x]

and

g (x) = x - [x]

, where

[\cdot]

, denotes greatest integer function, then which of the following is the zero function?

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 30

If

f (x) = \frac{x}{x - 1}, x \neq 1

, then

\underset{19 times}{\underset{⏟}{(f \circ f \circ \dots \circ f)}} (x)

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 31

Let,

f (x + \frac{1}{x}) = x^{2} + \frac{1}{x^{2}}, x \in R - \{0\}

, then

f (x)

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 32

Let,

f : [0, 1] \to [0, 1]

and

g : [0, 1] \to [0, 1]

be two functions defined by

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

and

g (x) = 4 x (1 - x)

, then

(f o g) (x)

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Target Exercises>Q 33

Let,

f (x) = | x - 1 |, x \in R

, then