Find f(g(x)) f(x)=x^2+7 , g(x) = square root of 8-x

$f (x) = x^{2} + 7$ , $g (x) = \sqrt{8 - x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\sqrt{8 - x})$ by substituting in the value of $g$ into $f$ .

$f (\sqrt{8 - x}) = {(\sqrt{8 - x})}^{2} + 7$

Step 3

Rewrite ${\sqrt{8 - x}}^{2}$ as $8 - x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 - x}$ as ${(8 - x)}^{\frac{1}{2}}$ .

$f (\sqrt{8 - x}) = {({(8 - x)}^{\frac{1}{2}})}^{2} + 7$

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

$f (\sqrt{8 - x}) = {(8 - x)}^{\frac{1}{2} \cdot 2} + 7$

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

$f (\sqrt{8 - x}) = {(8 - x)}^{\frac{2}{2}} + 7$

Cancel the common factor of $2$ .

Cancel the common factor.

$f (\sqrt{8 - x}) = {(8 - x)}^{\frac{2}{2}} + 7$

Rewrite the expression.

$f (\sqrt{8 - x}) = (8 - x) + 7$

Simplify.

$f (\sqrt{8 - x}) = 8 - x + 7$

Step 4

Add $8$ and $7$ .

$f (\sqrt{8 - x}) = - x + 15$