Show that the function given by $\displaystyle f(x) = \frac{k}{x},\ f:\mathbb{R} - \{0\}\rightarrow \mathbb{R} - \{0\}$, where $\displaystyle k\in\mathbb{R}, k\neq 0$ is inverse of itself.
For two functions, g(x) and f(x), to be inverses of eachother, g(f(x))=x and f(g(x))=x
So if f(x) is it's own inverse, then f(f(x))=x and swapping the order, f(f(x))=x, which is the same identity.
So f(f(x))=$\displaystyle f\left(\frac{k}{x}\right)=\frac{k}{\frac{k}{x}}=\f rac{k}{\frac{k}{x}}*\frac{x}{x}=\frac{kx}{k}=x$