Final answer:
Yes, f(x) = -1/2x + 9/2 and g(x) = -2x + 9 are inverse functions because the composition of the two functions yields the identity function for each variable.
Step-by-step explanation:
To determine if f(x) is the inverse function of g(x), we need to check if g(f(x)) equals x and f(g(x)) equals x for all x in the domain of these functions. The functions f(x) = -1/2x + 9/2 and g(x) = -2x + 9 are given. Let's perform the compositions.
First, we'll compute g(f(x)):
g(f(x)) = g(-1/2x + 9/2) = -2(-1/2x + 9/2) + 9 = x - 9 + 9 = x
Second, we'll compute f(g(x)):
f(g(x)) = f(-2x + 9) = -1/2(-2x + 9) + 9/2 = x - 9/2 + 9/2 = x
Since both compositions result in x, f(x) and g(x) are indeed inverse functions.