Final answer:
The functions f(x) = 4x - 8 and g(x) = (x + 4) / 8 are not inverses of each other because f(g(x)) = x - 4 and g(f(x)) = x - 1/2, neither of which equals x.
Step-by-step explanation:
To decide whether two functions are inverses of each other, you need to check if applying one function after the other returns the original input. For the functions given, f(x) = 4x - 8 and g(x) = (x + 4) / 8, we must determine if f(g(x)) = x and g(f(x)) = x for all values of x in the domain.
First, let's evaluate f(g(x)):
f(g(x)) = f((x + 4) / 8)f(g(x)) = 4((x + 4) / 8) - 8f(g(x)) = (x + 4) - 8f(g(x)) = x - 4
Now, let's evaluate g(f(x)):
g(f(x)) = g(4x - 8)g(f(x)) = (4x - 8 + 4) / 8g(f(x)) = (4x - 4) / 8g(f(x)) = x - 1/2
In both cases, the result is not simply x, so f(x) and g(x) are not inverses of each other.