# Let f(x)=4x+2 and g(x)=3x^2+3x. After simplifying, (f@g)(x)=?

Let $f\left(x\right)=4x+2$ and $g\left(x\right)=3{x}^{2}+3x$.
After simplifying, $\left(f\circ g\right)\left(x\right)=?$
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Compute the composite function as,
$f\circ g\left(x\right)=f\left(g\left(x\right)\right)$
$=f\left(3{x}^{2}+3x\right)$
$4\left(3{x}^{2}+3x\right)+2$
$=12{x}^{2}+12x+2$
Hence, the composite function $f\circ g\left(x\right)$ is,
$f\circ g\left(x\right)=12{x}^{2}+12x+2$