Which of the following function is invertible

Let the function $f$ be defined by $f(x) = \frac{{2x + 1}}{{1 - 3x}}$, then ${f^{ - 1}}(x)$ is

Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ and $g:\{a, b, c\} \rightarrow$ $\{$ apple, ball, cat $\}$ defined as $f(1)=a$, $f(2)=b$,  $f(3)=c$,  $g(a)=$ apple, $g(b)=$ ball and $g(c)=$ cat. Show that $f,\, g$ and $gof$ are invertible. Find out $f^{-1}, \,g^{-1}$ and $(gof)^{-1}$ and show that $(gof)^{-1}=f^{-1}og^{-1}$

Let $f: W \rightarrow W$ be defined as $f(n)=n-1,$ if 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.

If $f(x) = 3x - 5$, then ${f^{ - 1}}(x)$

The inverse of the function $\frac{{{{10}^x} - {{10}^{ - x}}}}{{{{10}^x} + {{10}^{ - x}}}}$ is