Question

Which two functions are inverses of each other?

1) f(x) = 4x and g(x) = 1/4x
2) f(x) = 1/4x and g(x) = 4x
3) f(x) = 2x and g(x) = 1/2x
4) f(x) = 1/2x and g(x) = 2x

Answer 1

The two functions that are inverses of each other are f(x) = 4x and g(x) = 1/4x.

Step-by-step explanation:

The two functions that are inverses of each other are f(x) = 4x and g(x) = 1/4x.

To determine if two functions are inverses, we need to show that when we apply one function followed by the other, we get back to the original input. In this case, if we apply the function f(x) = 4x and then g(x) = 1/4x, we get:

f(g(x)) = f(1/4x) = 4(1/4x) = x

Similarly, if we apply the function g(x) = 1/4x and then f(x) = 4x, we get:

g(f(x)) = g(4x) = 1/(4(4x)) = x

Therefore, f(x) = 4x and g(x) = 1/4x are inverse functions of each other.