Question

let $f(x) = 3x + 2$ and $g(x) = 2x^2 + 3x$. after simplifying, $(f \circ g)(x) = \square$ $(g \circ f)(x) = \square$ question help: \\(\boldsymbol{\text{message instructor}}\\)

Explanation:

Step1: Find \((f \circ g)(x)\)

The composition \((f \circ g)(x)\) means \(f(g(x))\). We substitute \(g(x)\) into \(f(x)\). Given \(f(x)=3x + 2\) and \(g(x)=2x^{2}+3x\), so we replace \(x\) in \(f(x)\) with \(2x^{2}+3x\).

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Step2: Find \((g \circ f)(x)\)

The composition \((g \circ f)(x)\) means \(g(f(x))\). We substitute \(f(x)\) into \(g(x)\). Given \(g(x)=2x^{2}+3x\) and \(f(x)=3x + 2\), so we replace \(x\) in \(g(x)\) with \(3x + 2\).

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Answer:

\((f \circ g)(x)=\boldsymbol{6x^{2}+9x + 2}\)
\((g \circ f)(x)=\boldsymbol{18x^{2}+33x + 14}\)