Which of the following function is inverse function
$f(x) = \frac{1}{{x - 1}}$
$f(x) = {x^2}$ for all$x$
$f(x) = {x^2}$, $x \ge 0$
$f(x) = {x^2},\;x \le 0$
If $y = f(x) = \frac{{x + 2}}{{x - 1}}$, then $x = $
Let $S=\{a, b, c\}$ and $T=\{1,2,3\} .$ Find $F^{-1}$ of the following functions $F$ from $S$ to $T$. if it exists. $F =\{( a , 2)\,,(b , 1),\,( c , 1)\}$
It is easy to see that $f$ is one-one and onto, so that $f$ is invertible with the inverse $f^{-1}$ of $f$ given by $f^{-1}=\{(1,2),(2,1),(3,1)\}=f$
The inverse function of $f(\mathrm{x})=\frac{8^{2 \mathrm{x}}-8^{-2 \mathrm{x}}}{8^{2 \mathrm{x}}+8^{-2 \mathrm{x}}}, \mathrm{x} \in(-1,1),$ is
Let $Y =\left\{n^{2}: n \in N \right\} \subset N .$ Consider $f: N \rightarrow Y$ as $f(n)=n^{2}$ Show that $f$ is invertible. Find the inverse of $f$