Question

If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).

A. (f + g)(x) = 5x + 11
B. (f + g)(x) = –3x + 5
C. (f + g)(x) = –5x – 11
D. (f + g)(x) = 3x – 5

Answer 1

`\huge\boxed{\sf (f + g)(x) = -3x + 5}`

Explanation:

Given functions:

• f(x) = x + 8
• g(x) = -4x - 3

Solution:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

`\rule[225]{225}{2}`

Answer 2

B

Explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5