If $f : R \to R$ is defined by $f(x) = x^2 + 1$,then $f^{-1}(17)$ and $f^{-1}(-3)$ are

Let $f(x)=(x+1)^2-1, x \geqslant-1$,then the set $\{x : f(x)=f^{-1}(x)\}$ is

Let $f: W \rightarrow W$ be defined as $f(n) = n-1$ if $n$ is odd and $f(n) = n+1$ if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$. Here,$W$ is the set of all whole numbers.

Let $S = \{a, b, c\}$ and $T = \{1, 2, 3\}$. Find $F^{-1}$ of the following function $F$ from $S$ to $T$,if it exists: $F = \{(a, 3), (b, 2), (c, 1)\}$.

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 $f:[1, \infty) \rightarrow [0, \infty)$ is given by $f(x) = x - \frac{1}{x}$, then $f^{-1}(x) =$