Algebra Examples

$f (x) = 3 x - 4$ $g (x) = \frac{x + 3}{4}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x + 3}{4})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x + 3}{4}) = 3 (\frac{x + 3}{4}) - 4$

Step 3

Combine $3$ and $\frac{x + 3}{4}$ .

$f (\frac{x + 3}{4}) = \frac{3 (x + 3)}{4} - 4$

Step 4

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$f (\frac{x + 3}{4}) = \frac{3 (x + 3)}{4} - 4 \cdot \frac{4}{4}$

Step 5

Simplify terms.

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Step 5.1

Combine $- 4$ and $\frac{4}{4}$ .

$f (\frac{x + 3}{4}) = \frac{3 (x + 3)}{4} + \frac{- 4 \cdot 4}{4}$

Step 5.2

Combine the numerators over the common denominator.

$f (\frac{x + 3}{4}) = \frac{3 (x + 3) - 4 \cdot 4}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$f (\frac{x + 3}{4}) = \frac{3 x + 3 \cdot 3 - 4 \cdot 4}{4}$

Step 6.2

Multiply $3$ by $3$ .

$f (\frac{x + 3}{4}) = \frac{3 x + 9 - 4 \cdot 4}{4}$

Step 6.3

Multiply $- 4$ by $4$ .

$f (\frac{x + 3}{4}) = \frac{3 x + 9 - 16}{4}$

Step 6.4

Subtract $16$ from $9$ .

$f (\frac{x + 3}{4}) = \frac{3 x - 7}{4}$