The function `f(x)=sin^(-1)(sinx)` , is

Options

A. continuous but not differentiable at `x=pi`
B. continuous and differentiable at x=0
C. discontinuous at `x=-pi`
D. none of these

Answer

B

Explanation

The graph of the function `f(x)=sin^(-1)(sin x)` is as shown in Fig.5

It is evident from the graph, of f(x) is everywhere continuous but not differentiable at `(2n+1)(pi)/(2), n in Z`
Also, f(x) is an odd function such that
`f'(x)=(-1)^(n),"if "(2n-1)(pi)/(2) lt x lt (2n+1)(pi)/(2)`