If `f:R to R ` be given by `f(x)= tan x,` then `f^(-1)(1)` is

Options

A. `(pi)/(4)`
B. `{n pi +(pi)/(4):n in Z}`
C. Does not exist
D. None of these

Answer

A

Explanation

Given that, `f(x)=tan x`
Let ` " " y= tanx implies x=tan^(-1)y`
`implies f^(-1)(x)=tan^(-1)ximpliesf^(-1)(1)=tan^(-1)1`
`implies " " =tan^(-1)"tan"(pi)/(4)=(pi)/(4) " "[ :' "tan"(pi)/(4)=1]`