100-x is the self-inverse to itself.

The term "self-inverse" means that when a function is applied twice, it gives the original value. In other words, if f(x) is a function, then f(f(x)) = x for it to be self-inverse.

Given the function f(x) = 100 - x, we want to find the value of x such that f(f(x)) = x.

Let's solve this step by step:

1. First, apply the function f(x) to itself, we get f(f(x)) = f(100 - x).

2. Substituting f(x) = 100 - x into the equation, we get f(100 - x) = 100 - (100 - x) = x.

So, the function f(x) = 100 - x is self-inverse for all real numbers x.