Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 10

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Let $f, g$ and $h$ be real valued functions defined from $R$ to $R$ by
$f (x) = x^{2} - 1, \forall x \in R$

$g (x) = \sqrt{1 + x^{2}} \forall x \in R$

$h (x) = \{\begin{cases} 0, x < 0 \\ x, x \geq 0 \end{cases}$
then the composite function $(h o f o g) (x)$ 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>Assignment>Q 11

Let

g (x) = x - [x] - 1

and

f (x) = \{\begin{cases} - 1, x < 0 \\ 0, x = 0 \\ 1, x > 0 \end{cases}

, where

[.]

represents the greatest integer function then for all

x, f (g (x)) =

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 12

If $f (x) = \{\begin{cases} 1 + x^{2} & ; x \leq 1 \\ x + 1 & ; 1 < x \leq 2 \end{cases}$ and $g (x) = 1 - x;$ $- 2 \leq x \leq 1$

$f (g (x)) = \{\begin{cases} k - x; & - 1 \leq x < 0 \\ x^{2} - 2 x + k; & 0 \leq x \leq 1 \end{cases}$ , then $k$ equals

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

Let

f (x) = 3 \sin^{3} x + 4 x - \sin | x | + \log (1 + | x |)

be defined on the interval

[0, 1]

. The even extension of

f (x)

to the interval

[- 1, 0]

is

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

Let

f (x) = | \sin x | + | \cos x |, g (x) = \cos (\cos x) + \cos (\sin x)

,

h (x) = \{- \frac{x}{2}\} + \sin π x

, where

{}

represents the fractional function, then the fundamental period of

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

Identify the correct statement

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Gamma Question Bank for Engineering Mathematics>Chapter 18 - Relation and Functions>Assignment>Q 16

Consider that the graph of

y = f (x)

is symmetric about the lines

x = 2

and

x = 4

then the period of

f (x)

is

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

If

f (x)

is a real-valued function defined as

f (x) = \ln (1 - \sin x)

, then the graph of

f (x)

is

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

If

\tan a x + \cot a x

and

| \tan x | + | \cot x |

are periodic functions of the same fundamental period then

a

equals