Question

Find and simplify the expression f(3+ h) – f(3) if:

f(x) = x^2 - 2
A. 2x
B. 9h
C. 6h + h^2
D. h^2
E. 6

Answer 1

C

Explanation:

f(x) = x² - 2

to evaluate f(3 + h) substitute x = 3 + h into f(x) and similarly to evaluate f(3) substitute x = 3 into f(x) , then

f(3 + h) - f(3)

= (3 + h)² - 2 - (3² - 2) ← expand squared factor using FOIL

= 9 + 6h + h² - 2 - 9 + 2 ← collect like terms

= 6h + h²