Answer: To evaluate h(3x), we need to substitute 3x into the function h(y) = y³ - (4/8)y.
Replacing y with 3x, we have:
h(3x) = (3x)³ - (4/8)(3x)
Simplifying this expression:
h(3x) = 27x³ - (1/2)x
Therefore, h(3x) is equal to 27x³ - (1/2)x.
Moving on to evaluating g(x+2), we substitute x+2 into the function g(x) = 3x² - 6x + 8.
Replacing x with x+2, we have:
g(x+2) = 3(x+2)² - 6(x+2) + 8
Expanding and simplifying this expression:
g(x+2) = 3(x² + 4x + 4) - 6x - 12 + 8
g(x+2) = 3x² + 12x + 12 - 6x - 4
Combining like terms:
g(x+2) = 3x² + 6x + 8
Therefore, g(x+2) is equal to 3x² + 6x + 8.