Answer
$g(x)=5-\frac{7}{2}x$
Work Step by Step
We are given:
$f(x)=3x+1$
and:
$(f+g)(x)=6-\displaystyle \frac{1}{2}x$
Thus:
$g(x)=(f+g)(x)-f(x)$
$g(x)=6-\displaystyle \frac{1}{2}x-3x-1$
$g(x)=5-\frac{7}{2}x$
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