Which parent functions have inverses which are also functions?

Question

If any vertical line intersects a graph in at most one point, then that graph is the graph of a function.

Answer 1

If a parent function passes the horizontal line test, then its inverse will pass the vertical line test and be a function. Some examples:

1. Linear functions of the form y = mx + b have inverses that are also functions, except for y = k where k is any constant.
2. Some odd-degree polynomials, such as f(x) = x³ + 1, also have inverses that are functions, though the inverses of most polynomials are not functions
3. Exponentials and logs are inverses of one another and both are functions
4. Some rational functions of odd-degree, such as 1/x or 1/x³, also have have inverses that are functions, though most rational functions do not.