Question

How can you tell if 2 functions are inverses of each other?

A) Their slopes are equal.
B) Their domains are the same.
C) Their graphs are reflections of each other over the line y = x.
D) They have the same y-intercept.

Answer 1

To determine if two functions are inverses of each other, we need to check if their compositions result in the identity function.

Step-by-step explanation:

In order to determine if two functions are inverses of each other, we need to check if their compositions result in the identity function.

If f(x) and g(x) are two functions, then for them to be inverses of each other:

1. The composition f(g(x)) should equal x for all x in the domain of g.
2. The composition g(f(x)) should equal x for all x in the domain of f.

If both conditions are satisfied, then the two functions are inverses of each other.