Question

Let f(x) = 2x+8, g(x) = x² + 2x - 8,and h(x) = 3x - 6.

Perform the indicated operation. (Simplify as far as possible.)
(f+g)(x)

Answer 1

The sum of functions f(x) = 2x + 8 and g(x) = x^2 + 2x - 8 is given by (f+g)(x) = x^2 + 4x. This implies that adding the corresponding terms results in the simplified expression x^2 + 4x.

To find the sum of two functions (f+g)(x), you simply add the corresponding terms of the functions f(x) and g(x):

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

Given:

f(x) = 2x + 8

g(x) = x^2 + 2x - 8

Now, add the corresponding terms:

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

Combine like terms:

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

Simplify further:

(f+g)(x) = x^2 + 4x

So, (f+g)(x) = x^2 + 4x.

To find the sum (f+g)(x), add corresponding terms of functions f(x) and g(x). In this case, given f(x) = 2x + 8 and g(x) = x^2 + 2x - 8, combining terms yields (f+g)(x) = x^2 + 4x. The simplified expression represents the sum of the two functions.