EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2018>Q 14

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IMPORTANT

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Consider the function $y = \log_{a} (x + \sqrt{x^{2} + 1})$ $a > 0, a \neq 1$ . The inverse of the function

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Important Questions on Functions

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2020>Q 1

The domain of

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

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2020>Q 2

Let

f (x) = \sqrt{x^{2} - 3 x + 2}

and

g (x) = \sqrt{x}

be two given functions. If

S

be the domain of

f o g

and

T

be the domain of

g o f

, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2018>Q 3

The domain of definition of

f (x) = \sqrt{\frac{1 - | x |}{2 - | x |}}

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2020>Q 4

\int_{0}^{2} [x^{2}] d x

is equal to, where

[\cdot]

represents greatest integer function

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2020>Q 5

If $f : S \to R,$ where $S$ is the set of all non-singular matrices of order $2$ over $R$ and $f [(\begin{array}{l} a & b \\ c & d \end{array})] = a d - b c,$ then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2020>Q 6

Let

A = \{x \in R : - 1 \leq x \leq 1\}

and

f : A \to A

be a mapping defined by

f (x) = x |x|

. Then

f

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2019>Q 7

Let

f : R \to R

be defined by

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

for all

x \in R .

Then,

HARD

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 19 - Functions>WBJEE 2019>Q 8

Let

S, T, U

be three non-void sets and

f : S \to T, g : T \to U

be so that

g o f : S \to U

is surjective. Then,