Question

Use the functions h(x) = 2x + 5 and t(x) = 7x − 6 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

h(x) = 2x + 5 and t(x) = 7x − 6

Part A: Find (h + t)(x)
(h + t)(x) = 2x + 5 + 7x − 6
(h + t)(x) = 9x − 1

Part B: Find (h ⋅ t)(x).
(h ⋅ t)(x) = (2x + 5 ) ( 7x − 6)
(h ⋅ t)(x) = 14x^2 + 35x - 12x - 30
(h ⋅ t)(x) = 14x^2 + 23x - 30

Part C: Find h[t(x)].
h[t(x)] = 2(7x − 6) + 5
h[t(x)] = 14x − 12 + 5
h[t(x)] = 14x − 7