Chapter 3 - Exponents, Polynomials and Functions - 3.3 Composing Functions - 3.3 Exercises - Page 258: 30

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

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}