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. (3 points)

Part B: Find (h ⋅ t)(x). Show your work. (3 points)

Part C: Find h[t(x)]. Show your work. (4 points)

Answer 1

To do part A and B, note that functions are distributive, meaning (h+t)(x) = h(x)+t(x) and (h•t)(x) = h(x)•t(x).

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

B: (h•t)(x) = (2x - 5)•(6x + 4) = 12x^2 - 22x - 20

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