Find the range of `tan^(-1)((2x)/(1+x^2))` – InterviewSolution

1.	Find the range of `tan^(-1)((2x)/(1+x^2))`
Answer» First, we must get the range of `(2x)/(1+x^(2))=y` We have `yx^(2)-2x+y=0` Since x is real, `D ge 0, " i.e., "4-4y^(2) ge 0 " or " -1 le y le 1.` So, ` "tan"^(-1)(y) in [-(pi)/(4),(pi)/(4)]` (As `tan x` is an increasing function)

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