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Question

Range of the function f(x)=x1+x where x is {x} which denotes the fractional part function is

A
[0,1)
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B
[0,12]
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C
[0,12)
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D
(0,12)
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Solution

The correct option is C [0,12)
The maximum value of fractional part of x tends to 1 but is never 1 actually. Its lowest value is 0 though.

f(x)=1(1+{x})2.

This is always positive. So f(x) is an increasing function.

Hence minimum value of the function is at x=0. f(x)=0

Maximum value of f(x) is as {x} tends to 1. The limiting value of the fuction is 12 but it is never actually attained by the function

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