Let $f: R \rightarrow R$ be given by $f(x) = \tan x$. Then,$f^{-1}(1)$ is

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be differentiable functions such that $(f \circ g)(x) = x$. If $f(x) = 2x + \cos x + \sin^2 x$, then the value of $\sum_{n=1}^{99} g(1 + (2n - 1) \pi)$ is

Let $f : R \rightarrow R$ be defined by $f(x) = x^3 - 3x^2 + 3x - 2$. Then $f^{-1}(x)$ is given by:

If $f(x) = \frac{a^x - a^{-x}}{a^x + a^{-x}}$,where $a$ and $x$ satisfy the necessary conditions,then $f^{-1}(x) =$

Consider $f: \{1, 2, 3\} \rightarrow \{a, b, c\}$ given by $f(1) = a, f(2) = b$ and $f(3) = c$. Find $f^{-1}$ and show that $(f^{-1})^{-1} = f$.

If $f:[1, \infty) \rightarrow [2, \infty)$ is given by $f(x) = x + \frac{1}{x}$,then $f^{-1}(x)$ equals