Range of `f(x)=sin^(-1)x+tan^(-1)x+sec^(-1)x` is

Options

A. `((pi)/(4), (3pi)/(4))`
B. `[(pi)/(4), (3pi)/(4)]`
C. `{(pi)/(4), (3pi)/(4)}`
D. none of these

Answer

C

Explanation

`f(x) = sin^(-1) x + tan^(-1) x + sec^(-1) x`,
clearly, domain of `f(x) " is " x = +- 1`
Thus, the range is `{f(1), f(-1)}`, i.e., `{(pi)/(4), (3pi)/(4)}`