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Question

If f(x)=ex, then limx0f(f(x))1(f(x)) is equal to (where {x} denotes fractional part of x)

A
f(1)
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B
f(0)
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C
0
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D
Does not exist
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Solution

The correct option is A f(1)
Given, f(x)=ex
Then we need to find limx0f[f(x)]1(f(x))=____
limx0f[f(x)]1(f(x))=limx0[eex]1ex
=limx0e(ex×1ex)
=limx0e
=e ....(1)
Given f(x)=ex
Put x=1
f(1)=e1
=e ....(2)
From Equation (1) and (2), option A is correct.

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