Determine whether f(x) = 5x and g(x) = 0.2x are inverses of each other.

Question

Quizplus · Accepted Answer

To check whether two functions are inverses of each other, we need to verify that the composition of the two functions in both orders gets us back the input.

To see this, let's compute (f ∘ g)(x) and (g ∘ f)(x):

(f ∘ g)(x) = f(g(x)) = f(0.2x) = 5(0.2x) = x

(g ∘ f)(x) = g(f(x)) = g(5x) = 0.2(5x) = x

Since (f ∘ g)(x) = (g ∘ f)(x) = x for all values of x, we can conclude that f(x) = 5x and g(x) = 0.2x are inverses of each other. Therefore, the answer is B.

Determine Whether F(x) = 5x and G(x) = 0