# need to find the following function

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pnyv1

Mathematics

### Question Description

Suppose that the functions q and r are defined as follows: q(x)= x^2+7 r(x)= SQRT x+8. Find the following (r0q)(1) and (q0r)(1)

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$q(x)= x^2+7\\ \\ r(x)= \sqrt{x+8}\\ \\ (roq)(x)=r(q(x))\\ \\ (roq)(x)=r(x^2+7)\\ \\ (roq)(x)=\sqrt{x^2+7+8}\\ \\ (roq)(x)=\sqrt{x^2+15}\\ \\ To\hspace{5} find\hspace{5} (roq)(1),\hspace{5} put\hspace{5} x = 1\\ \\ (roq)(1)=\sqrt{1^2+15}\\ \\ (roq)(1)=\sqrt{1+15}\\ \\ (roq)(1)=\sqrt{16}\\ \\ (roq)(1)=4\\ \\$

$(qor)(x)=q(r(x))\\ \\ (qor)(x)=q(\sqrt{x+8})\\ \\ (qor)(x)=(\sqrt{x+8})^2+7\\ \\ (qor)(x)=x+8+7\\ \\ (qor)(x)=x+15\\ \\ To\hspace{5} find\hspace{5} (qor)(1),\hspace{5} put\hspace{5} x = 1\\ \\ (qor)(1)=1+15\\ \\ (qor)(1)=16\\$

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fulnzanve3 (279)
UIUC
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