Find q(r(x)) q(x)=x^2+5 r(x) = square root of x+3

$q (x) = x^{2} + 5$ $r (x) = \sqrt{x + 3}$

Step 1

Set up the composite result function.

$q (r (x))$

Step 2

Evaluate $q (\sqrt{x + 3})$ by substituting in the value of $r$ into $q$ .

$q (\sqrt{x + 3}) = {(\sqrt{x + 3})}^{2} + 5$

Step 3

Rewrite ${\sqrt{x + 3}}^{2}$ as $x + 3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 3}$ as ${(x + 3)}^{\frac{1}{2}}$ .

$q (\sqrt{x + 3}) = {({(x + 3)}^{\frac{1}{2}})}^{2} + 5$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$q (\sqrt{x + 3}) = {(x + 3)}^{\frac{1}{2} \cdot 2} + 5$

Combine $\frac{1}{2}$ and $2$ .

$q (\sqrt{x + 3}) = {(x + 3)}^{\frac{2}{2}} + 5$

Cancel the common factor of $2$ .

Cancel the common factor.

$q (\sqrt{x + 3}) = {(x + 3)}^{\frac{2}{2}} + 5$

Rewrite the expression.

$q (\sqrt{x + 3}) = (x + 3) + 5$

Simplify.

$q (\sqrt{x + 3}) = x + 3 + 5$

Step 4

Add $3$ and $5$ .

$q (\sqrt{x + 3}) = x + 8$