Algebra Examples

$f (x) = 3 x - 9$ $g (x) = \frac{x + 3}{9}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 3}{9})$ by substituting in the value of $g$ into $f$ .

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $9$ .

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

Step 3.2

Cancel the common factor.

$f (\frac{x + 3}{9}) = 3 (\frac{x + 3}{3 \cdot 3}) - 9$

Step 3.3

Rewrite the expression.

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

Step 4

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$f (\frac{x + 3}{9}) = \frac{x + 3}{3} - 9 \cdot \frac{3}{3}$

Step 5

Simplify terms.

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Step 5.1

Combine $- 9$ and $\frac{3}{3}$ .

$f (\frac{x + 3}{9}) = \frac{x + 3}{3} + \frac{- 9 \cdot 3}{3}$

Step 5.2

Combine the numerators over the common denominator.

$f (\frac{x + 3}{9}) = \frac{x + 3 - 9 \cdot 3}{3}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 9$ by $3$ .

$f (\frac{x + 3}{9}) = \frac{x + 3 - 27}{3}$

Step 6.2

Subtract $27$ from $3$ .

$f (\frac{x + 3}{9}) = \frac{x - 24}{3}$