Question

What is (f − g)(x)?

f(x) = x^4 − x^2 + 9

g(x) = x^3 + 3x^2 + 12

(f − g)(x) =

Answer 1

x^4 - x^3 - 4x^2 - 3.

Explanation:

(f - g)(x) = f(x) - g(x)

= x^4 - x^2 + 9 - (x^3 + 3x^2 + 12)

Distributing the negative over the parentheses:

= x^4 - x^2 + 9 - x^3 - 3x^2 - 12

Simplifying like terms:

= x^4 - x^3 - 4x^2 - 3. (answer).