# Find the limits. lim_{xrightarrow-2} g(f(x)) f(x)=x+7 g(x)=x^2

Find the limits. $\underset{x\to -2}{lim}g\left(f\left(x\right)\right)$
$f\left(x\right)=x+7g\left(x\right)={x}^{2}$
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FieniChoonin
Given $f\left(x\right)=x+7$ and $g\left(x\right)={x}^{2}$ ,
To find limit of g(f(x)) first find the expression for g(f(x)) and then apply limit to the resulting expression.
We can g(f(x)) as follow:
$g\left(f\left(x\right)\right)=g\left(x+7\right)$
$g\left(x+7\right)=\left(x+7{\right)}^{2}$
$={x}^{2}+2\left(7\right)\left(x\right)+{7}^{2}$
$={x}^{2}+14x+49$
Therefore, $g\left(f\left(x\right)\right)={x}^{2}+14x+49$
We can the limit for the expression g(f(x)) as follows:
$\underset{x\to -2}{lim}g\left(f\left(x\right)\right)=\underset{x\to -2}{lim}\left({x}^{2}+14x+49\right)$
$=\left(-2{\right)}^{2}+14\left(-2\right)+49$
$=4-28+49=25$
Therefore $\underset{x\to -2}{lim}g\left(f\left(x\right)\right)=25$