Identify the function from the descriptions given below-1- Its domain is R and Range is -0-1 2- f x - x- if x -0-13- f x -0 if x - I set of integers4- f x -1- x if x -1-05- f x is periodic with period 1A- Greatest integer functionB- Least integer functionC- x-x-D- Fractional part functionE- -sin x -

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Monotonicity

Identify the ...

Question

Identify the function from the descriptions given below.

1. Its domain is R and Range is [0, 1)

2. f(x) = x, if x $ϵ$ [0, 1)

3. f(x) = 0 if x $ϵ$ I (set of integers)

4. f(x) = 1 + x if x $ϵ$ [-1, 0)

5. f(x) is periodic with period 1

Greatest integer function

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Least integer function

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x - [x]

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Fractional part function

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|sin x|

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Solution

The correct options are
C
x - [x]

D
Fractional part function

Options C and D are same.

(Fractional part of a function is defined as x - [x]

Ranges of the functions in A, B and E are not [0, 1). So the answers are C and D.

{x} is periodic with period 1. We can easily understand from its graph.

In the interval [-1, 0), [x] = -1

$\Rightarrow$ {x} = x - [x]

= x - (-1) = 1 + x

This is the 4th condition given, {x} satisfy all the other conditions given.

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Identify the function from the descriptions given below. 1. Its domain is R and Range is [0, 1) 2. f(x) = x, if x ϵ [0, 1) 3. f(x) = 0 if x ϵ I (set of integers) 4. f(x) = 1 + x if x ϵ [-1, 0) 5. f(x) is periodic with period 1

Identify the function from the descriptions given below.

1. Its domain is R and Range is [0, 1)

2. f(x) = x, if x $ϵ$ [0, 1)

3. f(x) = 0 if x $ϵ$ I (set of integers)

4. f(x) = 1 + x if x $ϵ$ [-1, 0)

5. f(x) is periodic with period 1