Question

Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below.

Part A: Find (a + b)(x). Show your work. (3 points)

Part B: Find (a ⋅ b)(x). Show your work. (3 points)

Part C: Find a[b(x)]. Show your work. (4 points)

(10 points)

Answer 1

For part A, you simply add the two functions a(x) and b(x). The resulting function is then (a+b)(x) = 5x +2.

For part B, you multiply the functions a(x) and b(x). Using the FOIL method, we obtain, 6x^2 -24x + 20x - 80. Simplifying, we get, (a*b)(x) = 6x^2 -4x - 80.

For part C, you replace x in the function a(x) with the expression from b(x). This results to: a[b(x)] = 3(2x - 8) +10. Simplifying, a[b(x)] = 6x - 14.