#### Answer

$f(g(x))=21x+14$

#### Work Step by Step

The student incorrectly defined the composition function to solve for $f(g(x)).$
With $f(x)=
3x-10
$ and $g(x)=
7x+8
,$ then by replacing $x$ with $g(x)$ in $f,$
\begin{array}{l}\require{cancel}
f(g(x))=f(7x+8)
\\\\
f(g(x))=3(7x+8)-10
\\\\
f(g(x))=21x+24-10
\\\\
f(g(x))=21x+14
.\end{array}