Find $f[g(x)]$ or $(f \circ g)(x)$
\[
\begin{array}{l}
f(x)=x^{2}+3 x \\
g(x)=x-2
\end{array}
\]

Answer

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Answer

$\boxed{f[g(x)] = x^2 - x - 2}$

Steps

Step 1 ：Let's find the composition of two functions, $f(x)$ and $g(x)$, denoted as $(f \circ g)(x)$ or $f[g(x)]$.

Step 2 ：We have $f(x)=x^{2}+3 x$ and $g(x)=x-2$.

Step 3 ：To find the composition of two functions, we substitute the second function, $g(x)$, into the first function, $f(x)$.

Step 4 ：Substitute $x-2$ (which is $g(x)$) into $f(x) = x^2 + 3x$.

Step 5 ：So, $f[g(x)] = (x-2)^2 + 3*(x-2)$

Step 6 ：Simplify the expression to get $f[g(x)] = x^2 - x - 2$.

Step 7 ：$\boxed{f[g(x)] = x^2 - x - 2}$