Finite Math Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\sqrt{x + 7})$ by substituting in the value of $g$ into $f$ .

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

Step 3

Rewrite ${\sqrt{x + 7}}^{2}$ as $x + 7$ .

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 7}$ as ${(x + 7)}^{\frac{1}{2}}$ .

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

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

Step 3.5

Simplify.

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

Step 4

Combine the opposite terms in $x + 7 - 7$ .

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Step 4.1

Subtract $7$ from $7$ .

$f (\sqrt{x + 7}) = x + 0$

Step 4.2

Add $x$ and $0$ .

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