Question

Use the functions h(x) = 2x - 5 and t(x) = 6x + 4 to complete the function operations listed below.

Part A: Find (h + t)(x). Show your work.
Part B: Find (h. t)(x). Show your work.
Part C: Find h[t(x)]. Show your work.

Answer 1

See below for answers (in bold) and explanations

Explanation:

Part A: (h+t)(x) = h(x) + t(x) = (2x-5) + (6x+4) = 2x - 5 + 6x + 4 = 8x - 1

Part B: (h*t)(x) = h(x) * t(x) = (2x-5) * (6x+4) = (2x)(6x) + (2x)(4) + (-5)(6x) + (-5)(4) = 12x² + 8x - 30x - 20 = 12x² - 22x - 20

Part C: h(t(x)) = h(6x + 4) = 2(6x + 4) - 5 = 12x + 8 - 5 = 12x + 3