Question

If f(x) = x/2 - 2 and g(x) = 2x² + x - 3, find (f+g)(x).

A) x² - 6
B) 2x² + 3/2x + 1
C) 2x² + 3/2x - 5
D) 2x² - x/2 + 1

Answer 1

To find (f+g)(x), add f(x) and g(x) to get 2x² + (3/2)x - 5. Thus, the correct answer is C) 2x² + 3/2x - 5.

Step-by-step explanation:

To find (f+g)(x), you simply add together the functions f(x) and g(x).

Given f(x) = x/2 - 2 and g(x) = 2x² + x - 3, the sum of the two functions is:
(f+g)(x) = (x/2 - 2) + (2x² + x - 3).

Combining like terms gives us:
(f+g)(x) = 2x² + (x/2 + x) - (2 + 3)
(f+g)(x) = 2x² + (1/2 + 1)x - 5
(f+g)(x) = 2x² + (3/2)x - 5.

Therefore, the correct answer is C) 2x² + 3/2x - 5.