Question

Identify the pair of functions that are inverses of each other.

A. f(x) = 5 + x and g(x) = 5 - x
B. f(x) = 2x - 9 and g(x) = (x + 9) / 2
C. f(x) = 2x - 6 and g(x) = x²
D. f(x) = 3 + 4x and g(x) = 3x - 4

Answer 1

Option B, f(x) = 2x - 9 and g(x) = (x + 9) / 2, represents a pair of functions that are inverses of each other since applying g after f, or f after g, returns the original input value.

Step-by-step explanation:

To identify the pair of functions that are inverses of each other, we look for two functions such that applying one after the other returns the original input. The inverse function "undoes" the effect of the original function.

In option B, f(x) = 2x - 9 and g(x) = (x + 9) / 2, we can see that g(f(x)) will return the original input x:

• Let y = f(x), so y = 2x - 9.
• Applying function g, g(y) = (y + 9) / 2 = ((2x - 9) + 9) / 2 = (2x) / 2 = x.

Similarly, f(g(x)) will return x as well:

• Let z = g(x), so z = (x + 9) / 2.
• Applying function f, f(z) = 2z - 9 = 2((x + 9) / 2) - 9 = x + 9 - 9 = x.

Therefore, functions f and g in option B are indeed inverses of each other since applying one function to the outcome of the other provides us with the original input value.