Final answer:
The functions h(x) = -1/3x + 1/3 and f(x) = -3x + 1 are inverses of each other.
Step-by-step explanation:
To determine if two functions are inverses of each other, we can check if their composition results in the identity function. Let's find the composition of h(x) and f(x):
h(f(x)) = -1/3(-3x + 1) + 1/3 = x - 1/3 + 1/3 = x.
Similarly, let's find the composition of f(h(x)):
f(h(x)) = -3(-1/3x + 1/3) + 1 = x - 1 + 1 = x.
Since h(f(x)) = x and f(h(x)) = x, we can conclude that h(x) and f(x) are inverses of each other.