Basic Operations
Subtracting Functions
To subtract functions, first change the sign of every term being subtracted using the Distributive Property. Eliminate the parentheses and combine like terms.Example Given f(x) = 3x2 +4x – 5 and g(x) = 2x2 - 6x + 5, find f(x) - g(x).
Step 1. Replace f(x) and g(x) with their equivalent expressions.
f(x) - g(x)
(3x2 + 4x – 5) - (2x2 - 6x + 5)
Step 2. Use the Distributive Property to change the sign of every term in g(x).
(3x2 +4x – 5) + (- 2x2 + 6x – 5)
Step 3. Eliminate the parentheses and combine like terms.
3x2 +4x – 5 - 2x2 + 6x – 5
(3x2– 2x2) + (4x + 6x) + (-5 – 5)
x 2 + 10x – 10