Algebra Examples

$f (x) = 3 \sqrt{x - 4}$ , $g (x) = \frac{1}{9} x^{2} + 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{1}{9} x^{2} + 4)$ by substituting in the value of $g$ into $f$ .

$f (\frac{1}{9} x^{2} + 4) = 3 \sqrt{(\frac{1}{9} x^{2} + 4) - 4}$

Step 3

Combine $\frac{1}{9}$ and $x^{2}$ .

$f (\frac{1}{9} x^{2} + 4) = 3 \sqrt{\frac{x^{2}}{9} + 4 - 4}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $4$ from $4$ .

$f (\frac{1}{9} x^{2} + 4) = 3 \sqrt{\frac{x^{2}}{9} + 0}$

Step 4.2

Add $\frac{x^{2}}{9}$ and $0$ .

$f (\frac{1}{9} x^{2} + 4) = 3 \sqrt{\frac{x^{2}}{9}}$

Step 4.3

Rewrite $9$ as $3^{2}$ .

$f (\frac{1}{9} x^{2} + 4) = 3 \sqrt{\frac{x^{2}}{3^{2}}}$

Step 5

Rewrite $\frac{x^{2}}{3^{2}}$ as ${(\frac{x}{3})}^{2}$ .

$f (\frac{1}{9} x^{2} + 4) = 3 \sqrt{{(\frac{x}{3})}^{2}}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$f (\frac{1}{9} x^{2} + 4) = 3 (\frac{x}{3})$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

$f (\frac{1}{9} x^{2} + 4) = 3 (\frac{x}{3})$

Step 7.2

Rewrite the expression.

$f (\frac{1}{9} x^{2} + 4) = x$