Answer
$(f - g)(x) = - x^2 + 3x - 3$
Work Step by Step
This exercise asks us to subtract $g(x)$ from $f(x)$. Let's write out the problem:
$(f - g)(x) = f(x) - g(x) = (3x - 2) - (x^2 + 1)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$(f - g)(x) = f(x) - g(x) = 3x - 2 - x^2 - 1$
Combine like terms:
$(f - g)(x) = f(x) - g(x) = 3x - x^2 - 3$
Rewrite in a more conventional form in terms of decreasing powers:
$(f - g)(x) = f(x) - g(x) = - x^2 + 3x - 3$
