Question

Which pair of functions are inverses of each other?

a) f(x) = m + 8 and g(x) = 6x - 8
b) f(x) = 32x and g(x) = x/32
c) f(x) = 5x - 11 and g(x) = 0 + 11
d) f(x) = 1 - 9 and g(x) = 29

Answer 1

The pair of functions that are inverses of each other is f(x) = 32x and g(x) = x/32, as their composition f(g(x)) and g(f(x)) equals x, confirming their inverse relationship.

Step-by-step explanation:

The functions f(x) = 32x and g(x) = x/32 are inverses of each other. When f and g are composed, they will cancel each other out, meaning f(g(x)) = g(f(x)) = x.

For example, if you substitute x with some number in g(x), and then apply the resulting value to f(x), you will end up with your original number. Similarly, applying f(x) to a number and then g(x) to the result gets you back to the original number. To further illustrate:

• f(g(x)) = f(x/32) = 32*(x/32) = x
• g(f(x)) = g(32x) = (32x)/32 = x

Since the composition of f and g yields the identity function, we have shown that they are indeed inverses of each other.