Answer
$h(x) + g(x) = -\frac{3}{2}x+ 11$
Work Step by Step
In this problem, we are asked to add two functions. Let us go ahead and set up the addition problem, separating the two functions with parentheses:
$h(x) + g(x) = (-2x + 4) + (\frac{1}{2}x + 7)$
Remove the parentheses, but pay attention to the operation in front of the parentheses:
$h(x) + g(x) = -2x + 4 + \frac{1}{2}x + 7$
Group like terms:
$h(x) + g(x) = (-2x + \frac{1}{2}x) + (4 + 7)$
Subtract fractions by finding equivalent fractions that have the same denominator:
$h(x) + g(x) = (-\frac{4}{2}x + \frac{1}{2}x) + (4 + 7)$
Combine like terms:
$h(x) + g(x) = -\frac{3}{2}x+ 11$
