If $f: R \rightarrow R$ is defined by $f(x)=|x|$,then

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 $(f^{-1})^{-1} = f$.

Which of the following functions cannot have their inverse defined? (where $[.] \to$ greatest integer function)

If $f(x) = (2x - 3\pi)^5 + \frac{4}{3}x + \cos x$ and $g$ is the inverse of $f$,then $g'(2\pi) = ?$

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

Let $f: N \rightarrow R$ be a function defined as $f(x)=4x^{2}+12x+15$. Show that $f: N \rightarrow S$,where $S$ is the range of $f$,is invertible. Find the inverse of $f$.