MATH SOLVE

3 months ago

Q:
# 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)

Accepted Solution

A:

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

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