Question

Create a rule you can use to determine whether two functions represent inverses of each other.

a) If the product of the functions is 1 for all inputs.
b) If the functions have the same slope and y-intercept.
c) If the composition of the functions results in the identity function.
d) If the functions have the same degree.

Answer 1

The rule to determine whether two functions represent inverses is if the composition of the functions results in the identity function.

Step-by-step explanation:

To determine whether two functions represent inverses of each other, we can use the rule of composition. If the composition of the functions results in the identity function, then they are inverses.

For example, let's say we have two functions f(x) and g(x), where f(g(x)) = x and g(f(x)) = x for all values of x. In this case, f and g are inverse functions.

So, the correct rule is c) If the composition of the functions results in the identity function. This means that when you plug one function into the other and simplify, you should end up with the original input value.