Question

What is f(g(x)) when f(x) = x2 + 5, and g(x) = 10 - 5x?

A) f(g(x)) = -5x2 + 35
B) f(g(x)) = -5x2 + 15
C) f(g(x)) = 25x2 + 105
D) f(g(x)) = 25x2 - 100x + 105

Answer 1

D

Explanation:

To obtain f(g(x)) substitute x = g(x) into f(x), that is

f(10 - 5x)

= (10 - 5x)² + 5 ← expand (10 - 5x)²

= 100 - 50x - 50x + 25x² + 5 ← collect like terms

= 25x² - 100x + 105 → D