Finite Math Examples

$f (x) = - 4 - 4$ , $g (x) = \frac{5}{4} x - 5$ , $(g \circ f)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (- 4 - 4)$ by substituting in the value of $f$ into $g$ .

$g (- 4 - 4) = \frac{5}{4} \cdot (- 4 - 4) - 5$

Step 3

Simplify each term.

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Step 3.1

Subtract $4$ from $- 4$ .

$g (- 4 - 4) = \frac{5}{4} \cdot - 8 - 5$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $- 8$ .

$g (- 4 - 4) = \frac{5}{4} \cdot (4 (- 2)) - 5$

Step 3.2.2

Cancel the common factor.

$g (- 4 - 4) = \frac{5}{4} \cdot (4 \cdot - 2) - 5$

Step 3.2.3

Rewrite the expression.

$g (- 4 - 4) = 5 \cdot - 2 - 5$

Step 3.3

Multiply $5$ by $- 2$ .

$g (- 4 - 4) = - 10 - 5$

Step 4

Subtract $5$ from $- 10$ .

$g (- 4 - 4) = - 15$