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Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),...

Given `f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0}`
` g(x) = {{:(f({x})",","for",n lt x lt n + (1)/(2)),(f(1-{x})",","for",n + (1)/(2) le x lt n + 1"," n in I),("",,{("where {x} denotes"),("fractional part function"):}),((5)/(2)"otherwise"",","",):}` then g(x) is

A

discontinuous at all integral values of x only

B

continuous everywhere except for x = 0

C

discontinuous at `x = n + (1)/(2), n in I` and at some `x in I`

D

continuous everywhere

Text Solution

Verified by Experts

The correct Answer is:
D
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