If `f(x)=sin^(-1) ((2x)/(1+x^2))` then `f(x)` is differentiable on

Options

A. `[-1,1]`
B. `R-{-1,1}`
C. `R- (-1,1) `
D. None of these

Answer

B

Explanation

Given , ` f(x) = sin^(-1)((2x)/(1 + x^(2)))`
On differentiating both sides w.r.t.x, we get
`f(x) = (1)/(sqrt(1 - ((2x)/(1 + x^(2)))))xx(d)/(dx)((2x)/(1 + x^(2)))`
`= (1+ x^(2))/(sqrt((1 - x^(2))^(2)) )xx(2 (1 - x^(2)))/((1 + x^(2))^(2))= (2)/(1 + x^(2)) xx(1 - x^(2))/(|1 - x^(2)|)`
`= {{:((2)/(1 + x^(2)),|x|lt 1 ),(- (2)/(1 + x^(2)),|x| gt 1 ):}`
`therefore f'(x) ` does not exist for ` |x| = 1 , "i.e.| x = pm 1`
Hence , f(x) is differentiable on ` R - { - 1, 1}` .