Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 22

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Which of the following pair of functions are identical ?

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Important Questions on Functions

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 23

If domain of

f (x)

is

(- \infty, 0],

then domain of

f (6 {x}^{2} - 5 {x} + 1)

is (where {.} represents fractional part function).

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

Let

f : (e, \infty) \to R

be defined by

f (x) = \ln (\ln (\ln (x))),

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 25

If

f (x) = 2 [x] + \cos x,

then

f : R \to R

is: (where

[.]

denotes greatest integer function)

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 26

If

f : R \to R

be a function such that

f (x) = \{\begin{cases} x | x | - 4; x \in Q \\ x | x | - \sqrt{3}; x \notin Q \end{cases}

, then

f (x)

is right.

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 27

f (x) = | x - 1 |

,

f : R^{+} \to R, g (x) = e^{x}, g : [- 1, \infty) \to R .

If the function

f \circ g (x)

is defined, then its domain and range respectively are:

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 28

Let

f : (2, 4) \to (1, 3)

be a function defined by

f (x) = x - [\frac{x}{2}]

(where

[.]

denotes the greatest integer function), then

f^{- 1} (x)

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 29

The mapping

f : R \to R

given by

f (x) = x^{3} + a x^{2} + b x + c

is a bijection if

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-2>Q 30

If the function

f : [1, \infty) \to [1, \infty)

is defined by

f (x) = 2^{x (x - 1)}

then

f^{- 1}

is