Question

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

Answer 1

For this case we have the following functions:
 h (x) = 2x - 5
 t (x) = 6x + 4

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

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

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