Algebra Examples

$f (x) = \frac{2}{3} x + 7$ $g (x) = 2 x + 15$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{2}{3} x + 7)$ by substituting in the value of $f$ into $g$ .

$g (\frac{2}{3} x + 7) = 2 (\frac{2}{3} x + 7) + 15$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{2}{3}$ and $x$ .

$g (\frac{2}{3} x + 7) = 2 (\frac{2 x}{3} + 7) + 15$

Step 3.2

Apply the distributive property.

$g (\frac{2}{3} x + 7) = 2 (\frac{2 x}{3}) + 2 \cdot 7 + 15$

Step 3.3

Multiply $2 \frac{2 x}{3}$ .

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Step 3.3.1

Combine $2$ and $\frac{2 x}{3}$ .

$g (\frac{2}{3} x + 7) = \frac{2 (2 x)}{3} + 2 \cdot 7 + 15$

Step 3.3.2

Multiply $2$ by $2$ .

$g (\frac{2}{3} x + 7) = \frac{4 x}{3} + 2 \cdot 7 + 15$

Step 3.4

Multiply $2$ by $7$ .

$g (\frac{2}{3} x + 7) = \frac{4 x}{3} + 14 + 15$

Step 4

Add $14$ and $15$ .

$g (\frac{2}{3} x + 7) = \frac{4 x}{3} + 29$