Finite Math Examples

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{2}{3} x - 6)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

Apply the distributive property.

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

$f (\frac{2}{3} x - 6) = \frac{1}{2} \cdot (2 x) + \frac{3}{2} \cdot - 6 + 6$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Factor $2$ out of $2 x$ .

$f (\frac{2}{3} x - 6) = \frac{1}{2} \cdot (2 (x)) + \frac{3}{2} \cdot - 6 + 6$

Step 3.4.2

Cancel the common factor.

$f (\frac{2}{3} x - 6) = \frac{1}{2} \cdot (2 x) + \frac{3}{2} \cdot - 6 + 6$

Step 3.4.3

Rewrite the expression.

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

Step 3.5

Cancel the common factor of $2$ .

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Step 3.5.1

Factor $2$ out of $- 6$ .

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

Step 3.5.2

Cancel the common factor.

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

Step 3.5.3

Rewrite the expression.

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

Step 3.6

Multiply $3$ by $- 3$ .

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

Step 4

Add $- 9$ and $6$ .

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