Precalculus Examples

$f (x) = \sqrt{2 x + 4}$ , $g (x) = \sqrt{9 x - 16}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (\sqrt{2 x + 4}) = \sqrt{9 (\sqrt{2 x + 4}) - 16}$

Step 3

Factor $2$ out of $2 x + 4$ .

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Step 3.1

Factor $2$ out of $2 x$ .

$g (\sqrt{2 x + 4}) = \sqrt{9 \sqrt{2 (x) + 4} - 16}$

Step 3.2

Factor $2$ out of $4$ .

$g (\sqrt{2 x + 4}) = \sqrt{9 \sqrt{2 x + 2 \cdot 2} - 16}$

Step 3.3

Factor $2$ out of $2 x + 2 \cdot 2$ .

$g (\sqrt{2 x + 4}) = \sqrt{9 \sqrt{2 (x + 2)} - 16}$