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

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IMPORTANT

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If $f (x) = [x]$ and $g (x) = x - [x]$ , where $[\cdot]$ , denotes greatest integer function, then which of the following is the zero function?

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Important Questions on Fundamentals of Relation and 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

EASY

JEE Advanced

IMPORTANT

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

The domain of the function

f (x) = \frac{1}{\sqrt{| x | - x}}

is

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JEE Advanced

IMPORTANT

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

Let, for

a \neq a_{1} \neq 0, f (x) = a x^{2} + b x + c, g (x) = a_{1} x^{2} + b_{1} x + c_{1}

and

p (x) = f (x) - g (x)

. If

p (x) = 0

only for

x = - 1

and

p (- 2) = 2

, then the value of

p (2)

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Entrances Gallery>Q 3

Let,

f : N \to Y

be a function defined as

f (x) = 4 x + 3

. If

f

is invertible, then its inverse is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 2 - Fundamentals of Relation and Function>Entrances Gallery>Q 4

A real-valued function

f (x)

satisfies the functional equation

f (x - y) = f (x) f (y) - f (a - x) f (a + y),

where

a

is a given constant and

f (0) = 1, f (2 a - x)

is equal to