Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-1>Q 38

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Exhaustive set of value of $x$ satisfying $\log_{| x |} (x^{2} + x + 1) \geq 0$ is -

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Important Questions on Functions

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 2

f (x) > x; \forall x \in R

. Then the equation

f (f (x)) - x = 0

has

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 3

If

f (x) = 4 x^{3} - x^{2} - 2 x + 1

and

g (x) = \{\begin{matrix} \min \{f (t) : 0 \leq t \leq x\}; & 0 \leq x \leq 1 \\ 3 - x; & 1 < x \leq 2 \end{matrix}

then

g (\frac{1}{4}) + g (\frac{3}{4}) + g (\frac{5}{4})

has the value equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 4

f (x)

and

g (x)

are two functions defined for all real values of

x

.

f (x)

is an even function and

g (x)

is periodic function, then-

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 5

If

f (x)

is defined on

(0, 1)

, then the domain of definition of

f (e^{x}) + f (\ln |x|)

is

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 6

f (x) = [\begin{matrix} 2 x + 3 & x \leq 1 \\ a^{2} x + 1 & x > 1 \end{matrix}

values of

' a'

for which

f (x)

is injective is-

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 7

The solution set for

[x] \{x\} = 1

where

\{x\}

and

[x]

are fractional part & integral part of

x,

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 8

The graph of function $f (x)$ is as shown. adjacently. Then the graph of $\frac{1}{f (|x|)}$ is-

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Beta Question Bank for Engineering: Mathematics>Chapter 25 - Functions>EXERCISE-2>Q 9

The fundamental period of

\frac{|\sin x| + |\cos x|}{|\sin x - \cos x| + |\sin x + \cos x|}

is-