Algebra Examples

$f (x) = \sqrt{3 x}$ , $g (x) = \sqrt{27 x} - \sqrt{48}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\sqrt{27 x} - \sqrt{48})$ by substituting in the value of $g$ into $f$ .

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (\sqrt{27 x} - \sqrt{48})}$

Step 3

Rewrite $27 x$ as $3^{2} \cdot (3 x)$ .

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Step 3.1

Factor $9$ out of $27$ .

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (\sqrt{9 (3) x} - \sqrt{48})}$

Step 3.2

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

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (\sqrt{3^{2} \cdot (3 x)} - \sqrt{48})}$

Step 3.3

Add parentheses.

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (\sqrt{3^{2} \cdot (3 x)} - \sqrt{48})}$

Step 4

Pull terms out from under the radical.

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (3 \sqrt{3 x} - \sqrt{48})}$

Step 5

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 5.1

Factor $16$ out of $48$ .

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (3 \sqrt{3 x} - \sqrt{16 (3)})}$

Step 5.2

Rewrite $16$ as $4^{2}$ .

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (3 \sqrt{3 x} - \sqrt{4^{2} \cdot 3})}$

Step 6

Pull terms out from under the radical.

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (3 \sqrt{3 x} - (4 \sqrt{3}))}$

Step 7

Multiply $4$ by $- 1$ .

$f (\sqrt{27 x} - \sqrt{48}) = \sqrt{3 (3 \sqrt{3 x} - 4 \sqrt{3})}$