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Question
Mark the correct alternative in the following question:
Let f : R → R be given by f(x) = tanx. Then, f-1(1) is
Options
\[\frac{\pi}{4}\]
\[\left\{ n\pi + \frac{\pi}{4}: n \in Z \right\}\]
does not exist
none of these
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Solution
We have,
f : R → R is given by
f (x) = tan x
⇒ f-1 (x) = tan-1 x
∴ f-1 (1) = tan-1 1 = {nπ + π /4 : n ∈ Z}
Hence, the correct alternative is option (b).
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