Question

Let f(x) = 3x2 + x − 3 and g(x) = x2 − 5x + 1. Find f(x) − g(x).

Answer 1

f(x) - g(x) = 3x² + x - 3 - (x² - 5x + 1)
f(x) - g(x) = 3x² + x - 3 - x² + 5x - 1
f(x) - g(x) = 3x² - x² + x + 5x - 3 - 1
f(x) - g(x) = 2x² + 6x - 4

Answer 2

Substitute the two functions according to a given condition of function:
f(x) - g(x) = 3x² + x - 3 - (x² - 5x + 1)
= 3x² + x - 3 - x² + 5x - 1
= 2x² + 6x - 4  or  2(x² + 3x - 2)