Algebra Examples

$f (x) = x^{2} - 5$ $g (x) = \sqrt{5 - x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\sqrt{5 - x})$ by substituting in the value of $g$ into $f$ .

$f (\sqrt{5 - x}) = {(\sqrt{5 - x})}^{2} - 5$

Step 3

Rewrite ${\sqrt{5 - x}}^{2}$ as $5 - x$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 - x}$ as ${(5 - x)}^{\frac{1}{2}}$ .

$f (\sqrt{5 - x}) = {({(5 - x)}^{\frac{1}{2}})}^{2} - 5$

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

$f (\sqrt{5 - x}) = {(5 - x)}^{\frac{1}{2} \cdot 2} - 5$

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

$f (\sqrt{5 - x}) = {(5 - x)}^{\frac{2}{2}} - 5$

Cancel the common factor of $2$ .

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Cancel the common factor.

$f (\sqrt{5 - x}) = {(5 - x)}^{\frac{2}{2}} - 5$

Rewrite the expression.

$f (\sqrt{5 - x}) = (5 - x) - 5$

Simplify.

$f (\sqrt{5 - x}) = 5 - x - 5$

Step 4

Combine the opposite terms in $5 - x - 5$ .

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Subtract $5$ from $5$ .

$f (\sqrt{5 - x}) = - x + 0$

Add $- x$ and $0$ .

$f (\sqrt{5 - x}) = - x$