The function `f(x) = tan^(-1)(tanx)` is

Options

A. everywhere continuous
B. discontinuous at `x=(n pi)/(2), n in Z`
C. not differentiable at x
D. everywhere continuous and differentiable such that f'(x)=1 for all `x in R`

Answer

C

Explanation

The graph of the function `f(x)=tan^(-1)` (tan x) is as given in Fig. 7

It is evidently fromt the curve y=f(x) is discontinuous and hence non-differentiable at `x={(2n+1)(pi)/(2), n in Z}` such that `f'(x)=1"for all "x in R-{(2n+1)(pi)/(2), n in Z}`