Question

Let f--1 = 1/f

Find an example of such a function, where the domain of f
consistsof a single point.

Answer 1

For all real numbers x, define the function f by f(x)=0 if x≠1 and f(1)=2.

Explanation:

The domain of f is the set of real numbers (R). To define
`f^(-1)(x)=1/f(x)` at a point x, we need that f(x)≠0 as division by zero is undefined.

However, there is only one point x such that f(x)≠0, the point x=1.

Thus
`f^(-1)(1)=1/f(1)=1/2` and the domain of
`f^(-1)` is the set {1}.