Answer
$(f + g)(x) = x^2 + 3x - 1$
Work Step by Step
This exercise asks us to add $g(x)$ to $f(x)$. 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:
$(f + g)(x) = f(x) + g(x) = 3x + x^2 - 1$
Rewrite in a more conventional form in terms of decreasing powers:
$(f + g)(x) = f(x) + g(x) = x^2 + 3x - 1$
