##### need to find the following function

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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)

Jun 8th, 2015

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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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Jun 8th, 2015

$\frac{-1}{3x^2+4}$

Is this correct?

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Jun 8th, 2015

no it is not correct

Jun 8th, 2015

$\frac{-1}{3x^2}+4$

Is this correct?

Jun 8th, 2015

$\frac{-1}{3}x^2+4$

or like this?

Jun 8th, 2015

Jun 8th, 2015

Jun 8th, 2015

Jun 8th, 2015

I have another question now; Suppose that the relation G is defined as follows G={(-1,3),(3,1),(2,2),(0,-9)} Give the domain and range of G. Write  answer using set notation.

Jun 8th, 2015

Thank you. I appreciate it.

Jun 8th, 2015

:)

Jun 8th, 2015

Domain is all the x values and Range is all the y values.

Domain = {-1, 3, 2, 0}

Range = {3, 1, 2, -9}

Jun 8th, 2015

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Jun 8th, 2015
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Jun 8th, 2015
Oct 19th, 2017
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