# Let f(x) =x^2+9x and g(x) =9x+8 perform the composition or operation indicated below (f@g)(5) simplify the answer

Let $f\left(x\right)={x}^{2}+9x$ and $g\left(x\right)=9x+8$ perform the composition or operation indicated below $\left(f\circ g\right)\left(5\right)$ simplify the answer
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Alara Mccarthy
Let us first calculate the composite function of the two given functions which are
$f\left(x\right)={x}^{2}+9x$ and $g\left(x\right)=9x+8$
The composite function will be given by,
$\left(f\circ g\right)\left(x\right)$
$=f\left(g\left(x\right)\right)$
$={\left(9x+8\right)}^{2}+9\left(9x+8\right)$
$=\left(81{x}^{2}+144x+64+81x+72\right)$
$=81{x}^{2}+225x+136$
To calculate the required value, we need to substitute x=5 in the composite function obtained above. So we will have, $\left(f\circ g\right)\left(5\right)$
$=81{\left(5\right)}^{2}+225\left(5\right)+136$
=81(25)+1125+136
=2025+1261
=3286