Algebra Examples

$f (x) = 6 x - 3$ , $g (x) = \frac{x + 6}{3}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 6}{3})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 6}{3}) = 6 (\frac{x + 6}{3}) - 3$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $6$ .

$f (\frac{x + 6}{3}) = 3 (2) (\frac{x + 6}{3}) - 3$

Step 3.1.2

Cancel the common factor.

$f (\frac{x + 6}{3}) = 3 \cdot (2 (\frac{x + 6}{3})) - 3$

Step 3.1.3

Rewrite the expression.

$f (\frac{x + 6}{3}) = 2 (x + 6) - 3$

Step 3.2

Apply the distributive property.

$f (\frac{x + 6}{3}) = 2 x + 2 \cdot 6 - 3$

Step 3.3

Multiply $2$ by $6$ .

$f (\frac{x + 6}{3}) = 2 x + 12 - 3$

Step 4

Subtract $3$ from $12$ .

$f (\frac{x + 6}{3}) = 2 x + 9$