# Suppose that the dunctions q and r are defined as follows. q(x)=x^2+5 r(x)=sqrt(x+3) Find the following. q@r(1)=? (r@q)(1)=?

Suppose that the dunctions q and r are defined as follows.
$q\left(x\right)={x}^{2}+5$
$r\left(x\right)=\sqrt{x+3}$
Find the following.
$q\circ r\left(1\right)=?$
$\left(r\circ q\right)\left(1\right)=?$
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The composition of the function f(x) and g(x) is denoted by $f\circ g\left(x\right)$ is:
$\left(q\circ r\right)\left(1\right)=q\left(r\left(1\right)\right)$
$=q\left(\sqrt{1+3}\right)\left\{{:}^{\prime }r\left(x\right)=\sqrt{x+5}\right\}$
$=q\left(2\right)$
$={2}^{2}+5{}^{\prime }q\left(x\right)={x}^{2}+5\right\}$
=4+5
=9
Compute the value of composite function $\left(r\circ q\right)\left(1\right):$
$\left(r\circ q\right)\left(1\right)=r\left(q\left(1\right)\right)$
$=r\left({1}^{2}+5\right)\left\{{:}^{\prime }q\left(x\right)={x}^{2}+5\right\}$
$=r\left(6\right)$
$=\sqrt{6+5}\left\{{:}^{\prime }r\left(x\right)=\sqrt{x+5}\right\}$
$=\sqrt{11}$