Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.2>Q 13

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$f : A \to B$ such that $f (x) = \log_{2} \{\frac{(\sin x + \cos x) + 3 \sqrt{2}}{\sqrt{2}}\}$ is an onto function. Then $B$ is given by

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Important Questions on Relation and Functions

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.2>Q 14

Set

A

has

3

elements and set

B

has

4

elements. The number of injection that can be defined from

A

to

B

is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.2>Q 15

Let the function

f : R \to R

be defined by

f (x) = 2 x + \sin x, x \in R

. Then

f

is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.2>Q 17

The function

f : R \to R

defined by

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

is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.2>Q 18

Function

f : R \to R; f (x) = \frac{e^{x^{2}} - e^{- x^{2}}}{e^{x^{2}} + e^{- x^{2}}}

is

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.3>Q 19

If

f (x) = e^{2 x}

and

g (x) = \log \sqrt{x}, (x > 0)

, then

f o g (x)

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.3>Q 20

If

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

, then

(f o f o f) (x) =

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.3>Q 21

If

g (x) = x^{2} + x - 2

and

\frac{1}{2} g (f (x)) = 2 x^{2} - 5 x + 2

, then

f (x)

can be

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>EXERCISE 1.3>Q 22

Let the function

f

be defined by

f (x) = \frac{2 x + 1}{1 - 3 x}

then

f^{- 1} (x)

is: