Chapter 3 - Exponents, Polynomials and Functions - 3.3 Composing Functions - 3.3 Exercises - Page 258: 28

$g(f(x))=21x-62$

The student incorrectly omitted the expression $+8$ in his solution to get $g(f(x)).$ With $f(x)= 3x-10 $ and $g(x)= 7x+8 ,$ then by replacing $x$ with $f(x)$ in $g,$ \begin{array}{l}\require{cancel} g(f(x))=g(3x-10) \\\\ g(f(x))=7(3x-10)+8 \\\\ g(f(x))=21x-70+8 \\\\ g(f(x))=21x-62 .\end{array}