# Chapter 3 - Exponents, Polynomials and Functions - 3.3 Composing Functions - 3.3 Exercises - Page 259: 47

$\text{a) } f(x)g(x)=27x^2+69x+14 \\\\\text{b) } f(x)+g(x)=12x+9 \\\\\text{c) } f(g(x))=27x+65$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ Substitute the given functions, \begin{array}{l}\require{cancel} f(x)= 9x+2 \\g(x)= 3x+7 ,\end{array} into the required operations. $\bf{\text{Solution Details:}}$ a) \begin{array}{l}\require{cancel} f(x)g(x)=(9x+2)(3x+7) \\\\ f(x)g(x)=9x(3x)+9x(7)+2(3x)+2(7) \\\\ f(x)g(x)=27x^2+63x+6x+14 \\\\ f(x)g(x)=27x^2+69x+14 .\end{array} b) \begin{array}{l}\require{cancel} f(x)+g(x)=(9x+2)+(3x+7) \\\\ f(x)+g(x)=12x+9 .\end{array} c) \begin{array}{l}\require{cancel} f(g(x))=f(3x+7) \\\\ f(g(x))=9(3x+7)+2 \\\\ f(g(x))=27x+63+2 \\\\ f(g(x))=27x+65 .\end{array} Therefore, \begin{array}{l}\require{cancel} \text{a) } f(x)g(x)=27x^2+69x+14 \\\\\text{b) } f(x)+g(x)=12x+9 \\\\\text{c) } f(g(x))=27x+65 .\end{array}

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