Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 44

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Graph of $y = {x} + {- x}$ in the interval $[- 1, 2]$ is (where ${\cdot}$ denotes fractional part function).

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Important Questions on Functions

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 45

Number of integers satisfying the equation

[x] + [2 x] + [3 x] = {x} + {2 x} + 2 x^{2}

, (where [.] and

{.}

denotes greatest-integer function and fractional part function respectively) are

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 46

The number of solutions of equation

| [x] - 2 x | = 4

is (where

[\cdot]

represents the greatest integer function)

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 47

The complete solution set of the equation

Sgn (\frac{x^{2} - 5 x + 4}{\{x\}}) = - 1,

where

\{\cdot\}

is fractional part function, is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 48

Number of integral solutions of the equation

sgn (\sin x) = 1

in

[0, 10]

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 52

Represent all possible functions defined from

\{α, β\}

to

\{1, 2\}

.

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 53

Find the domain of the function $f (x) = \frac{1}{\log (2 - x)} + \sqrt{x + 1}$ .

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 54

Find the domain of the function $f (x) = \sqrt{1 - x} - \sin^{- 1} (\frac{2 x - 1}{3})$ .

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Alpha Question Bank for Engineering: Mathematics>Chapter 24 - Functions>Exercise-1>Q 55

Find domain and range of following function: $y = x^{3}$