Question

Use the functions f(x) = 2x + 7 and g(x) = 6x − 5 to complete the function operations listed below.

Answer 1

We are given the two functions:

f(x) = 2x + 7

g(x) = 6x – 5

 

Part A. Find (f + g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 2 x + 7 + 6 x – 5

(f + g)(x) = 8 x + 2

 

Part B. Find (f ⋅ g)(x)

(f ⋅ g)(x) = f(x) ⋅ g(x)

(f ⋅ g)(x) = (2 x + 7) (6 x – 5)

(f ⋅ g)(x) = 12 x^2 – 10 x + 42 x – 35

(f ⋅ g)(x) = 12 x^2 + 32 x – 35

 

Part C. Find f[g(x)]

f[g(x)] = 2 (6 x – 5) + 7

f[g(x)] = 12 x – 10 + 7

f[g(x)] = 12 x - 3