Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 50

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Let $D \equiv [- 1, 1]$ is the domain of the following functions, the state which of them are injective.

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Important Questions on Functions

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 51

The function

f : X \to Y

, defined by

f (x) = x^{2} - 4 x + 5

is both one-one and onto if

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 52

f : N \to N

where

f (x) = x - (- 1)^{x}

then

f

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 53

Which one of the following pair of functions are NOT identical?

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 54

If the graph of the function

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

is symmetric about

y -

axis, then

n

is equal to:

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 55

If

f (x) = \{\begin{cases} x^{2} & ; x \leq 1 \\ 1 - x & ; x > 1 \begin{array}{l}  \end{array} \end{cases}

and composite function

h (x) = | f (x) | + f (x + 2),

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 56

Let

f (x) = \{\begin{cases} \begin{array}{l} 0 for x = 0 \\ x^{2} \sin (\frac{π}{x}) for - 1 < x < 1 (x \neq 0) \end{array} \\ - |x| x for x > 1 or x < - 1 \end{cases}

, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 57

If

f : [- 2, 2] \to R

where

f (x) = x^{3} + \tan x + [\frac{x^{2} + 1}{P}]

is an odd function, then the value of parametric

P

, where

[.]

denotes the greatest integer function, can be

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 58

If

f : R \to [- 1, 1],

where

f (x) = \sin (\frac{π}{2} [x]),

(where

[.]

denotes the greatest integer function), then