Finite Math Examples

$f (x) = \frac{13}{5} x + 33$ , $g (x) = \frac{5}{13} \cdot (x - 33)$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{5}{13} \cdot (x - 33))$ by substituting in the value of $g$ into $f$ .

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot (\frac{5}{13} \cdot (x - 33)) + 33$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot (\frac{5}{13} x + \frac{5}{13} \cdot - 33) + 33$

Step 3.2

Combine $\frac{5}{13}$ and $x$ .

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot (\frac{5 x}{13} + \frac{5}{13} \cdot - 33) + 33$

Step 3.3

Multiply $\frac{5}{13} \cdot - 33$ .

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Step 3.3.1

Combine $\frac{5}{13}$ and $- 33$ .

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot (\frac{5 x}{13} + \frac{5 \cdot - 33}{13}) + 33$

Step 3.3.2

Multiply $5$ by $- 33$ .

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot (\frac{5 x}{13} + \frac{- 165}{13}) + 33$

Step 3.4

Move the negative in front of the fraction.

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot (\frac{5 x}{13} - \frac{165}{13}) + 33$

Step 3.5

Apply the distributive property.

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot \frac{5 x}{13} + \frac{13}{5} \cdot (- \frac{165}{13}) + 33$

Step 3.6

Cancel the common factor of $13$ .

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Step 3.6.1

Cancel the common factor.

$f (\frac{5}{13} \cdot (x - 33)) = \frac{13}{5} \cdot \frac{5 x}{13} + \frac{13}{5} \cdot (- \frac{165}{13}) + 33$

Step 3.6.2

Rewrite the expression.

$f (\frac{5}{13} \cdot (x - 33)) = \frac{1}{5} \cdot (5 x) + \frac{13}{5} \cdot (- \frac{165}{13}) + 33$

Step 3.7

Cancel the common factor of $5$ .

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Step 3.7.1

Factor $5$ out of $5 x$ .

$f (\frac{5}{13} \cdot (x - 33)) = \frac{1}{5} \cdot (5 (x)) + \frac{13}{5} \cdot (- \frac{165}{13}) + 33$

Step 3.7.2

Cancel the common factor.

$f (\frac{5}{13} \cdot (x - 33)) = \frac{1}{5} \cdot (5 x) + \frac{13}{5} \cdot (- \frac{165}{13}) + 33$

Step 3.7.3

Rewrite the expression.

$f (\frac{5}{13} \cdot (x - 33)) = x + \frac{13}{5} \cdot (- \frac{165}{13}) + 33$

Step 3.8

Cancel the common factor of $13$ .

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Step 3.8.1

Move the leading negative in $- \frac{165}{13}$ into the numerator.

$f (\frac{5}{13} \cdot (x - 33)) = x + \frac{13}{5} \cdot \frac{- 165}{13} + 33$

Step 3.8.2

Cancel the common factor.

$f (\frac{5}{13} \cdot (x - 33)) = x + \frac{13}{5} \cdot \frac{- 165}{13} + 33$

Step 3.8.3

Rewrite the expression.

$f (\frac{5}{13} \cdot (x - 33)) = x + \frac{1}{5} \cdot - 165 + 33$

Step 3.9

Cancel the common factor of $5$ .

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Step 3.9.1

Factor $5$ out of $- 165$ .

$f (\frac{5}{13} \cdot (x - 33)) = x + \frac{1}{5} \cdot (5 (- 33)) + 33$

Step 3.9.2

Cancel the common factor.

$f (\frac{5}{13} \cdot (x - 33)) = x + \frac{1}{5} \cdot (5 \cdot - 33) + 33$

Step 3.9.3

Rewrite the expression.

$f (\frac{5}{13} \cdot (x - 33)) = x - 33 + 33$

Step 4

Combine the opposite terms in $x - 33 + 33$ .

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Step 4.1

Add $- 33$ and $33$ .

$f (\frac{5}{13} \cdot (x - 33)) = x + 0$

Step 4.2

Add $x$ and $0$ .

$f (\frac{5}{13} \cdot (x - 33)) = x$