 # Suppose that the dunctions q and r are defined as follows.q(x)=x^2+7r(x)=sqrt(x+8)Find the following.q@r(1)=?(r@q)(1)=? Brennan Flores 2021-01-05 Answered

Suppose that the dunctions q and r are defined as follows.
$q\left(x\right)={x}^{2}+7$
$r\left(x\right)=\sqrt{x+8}$
Find the following.
$q\cdot r\left(1\right)=?$
$\left(r\cdot q\right)\left(1\right)=?$

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Find the function definition for the first composite function, as follows:
$\left(q\cdot r\right)\left(x\right)=q\left(r\left(x\right)\right)$
$=q\left(\sqrt{x+8}\right)$
$=\left({\sqrt{x+8}}^{2}+7\right)$
$=x+8+7$
$=x+15$
Find the function definition for the second composite function, as follows:
$\left(r\cdot q\right)\left(x\right)=r\left(q\left(x\right)\right)$
$=r\left({x}^{2}+7\right)$
$=\sqrt{\left({x}^{2}+7\right)+8}$
$=\sqrt{x+15}$
Find the value of the first composite function at x=1, as follows:
$\left(q\cdot r\right)\left(1\right)=\left(1\right)+15=16$
Find the value of the second composite function at x=1, as follows:
$\left(r\cdot q\right)\left(1\right)=\sqrt{{1}^{2}+15}$
$=\sqrt{16}$
=4

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