Question

Proof that an invertible function f can have only one inverse

Answer 1

Step-by-step explanation:

We remeber that If we compose a function and it's inverse,

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

A invertible function is one to one so suppose that we have two inverse, g(x) and h(x). Let plug them in ,

$f(h(x)$

and

$f(g(x)$

Since f is a invertible function, it is one to one so if g and h are both inverse of f, then they are eqaul

$f(h(x) = f(g(x)$

$h(x) = g(x)$

Thus, a invertible function can have only one inverse.