Question

I need quick! 20 points!

Answer 1

Given is h(x) = 4x − 5 and t(x) = 2x + 4.

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

Part B: Finding​ (h ⋅ t)(x)
$(h ⋅ t)(x) = (4x - 5)(2x + 4) \\ (h ⋅ t)(x) = 4x(2x + 4) - 5(2x + 4) \\ (h ⋅ t)(x) = 8 {x}^{2} + 16x - 10x - 20 \\ (h ⋅ t)(x) = 8 {x}^{2} + 6x - 20$
Part C: Finding h[t(x)]
$h[t(x)] = 4 \times t(x) - 5 \\ h[t(x)] = 4(2x + 4) - 5 \\ h[t(x)] = 8x + 16 - 5 \\ h[t(x)] = 8x + 11$