Given f(t) = t² - t and h(x) = 3x + 2, evaluate: a. h(f(2)) and b. h(f(-2)).a. h(f(2))h(f(2)) = h(2² - 2) = h(2)h(2) = 3(2) + 2 = 8.
Therefore, h(f(2)) = 8b. h(f(-2))h(f(-2)) = h((-2)² - (-2)) = h(4 + 2)h(f(-2)) = h(6) = 3(6) + 2 = 20.
Therefore, h(f(-2)) = 20
To find the value of h(f(2)), we need to first find the value of f(2), which can be done by substituting 2 in the given equation f(t) = t² - t. f(2) = 2² - 2 = 2.
Now we can substitute f(2) in h(x) to get h(f(2)). h(f(2)) = h(2) = 3(2) + 2 = 8.
Therefore, h(f(2)) = 8. Similarly, to find the value of h(f(-2)), we need to first find the value of f(-2), which can be done by substituting -2 in the given equation f(t) = t² - t. f(-2) = (-2)² - (-2) = 4 + 2 = 6.
Now we can substitute f(-2) in h(x) to get h(f(-2)). h(f(-2)) = h(6) = 3(6) + 2 = 20.
Therefore, h(f(-2)) = 20.
Therefore, h(f(2)) = 8 and h(f(-2)) = 20 are the answers.