Final answer:
To determine if two functions are inverses of each other, we need to check if their composition results in the identity function. In this case, the composition of h(x) and p(x) does not result in the identity function, so they are not inverses of each other.
Step-by-step explanation:
To determine if two functions are inverses of each other, we need to check if their composition, (h º p)(x), results in the identity function, which is represented by f(x) = x. In this case, we have h(x) = (3x - 4)/9 and p(x) = (3x + 4)/3. To find (h º p)(x), we substitute p(x) into h(x) and simplify.
(h º p)(x) = h(p(x)) = h((3x + 4)/3) = 3((3x + 4)/3) - 4)/9 = (9x + 12 - 4)/9 = (9x + 8)/9
Now we need to check if (h º p)(x) is equal to x. If (h º p)(x) = x, then the functions h(x) and p(x) are inverses of each other.
(h º p)(x) = x if (9x + 8)/9 = x
Let's solve for x:
9x + 8 = 9x
8 = 0
This is not a true statement, which means that (h º p)(x) is not equal to x. Therefore, the functions h(x) and p(x) are not inverses of each other.