Precalculus Examples

$f (x) = x + 5$ $g (x) = - x^{2} - 5 x$ Find $f (g (- 4))$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- x^{2} - 5 x)$ by substituting in the value of $g$ into $f$ .

$f (- x^{2} - 5 x) = (- x^{2} - 5 x) + 5$

Step 3

Remove parentheses.

$f (- x^{2} - 5 x) = - x^{2} - 5 x + 5$

Step 4

Evaluate the result function by replacing $x$ with $- 4$ in the function.

$- {(- 4)}^{2} - 5 \cdot - 4 + 5$

Step 5

Simplify the evaluated function.

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Step 5.1

Simplify each term.

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Step 5.1.1

Raise $- 4$ to the power of $2$ .

$- 1 \cdot 16 - 5 \cdot - 4 + 5$

Step 5.1.2

Multiply $- 1$ by $16$ .

$- 16 - 5 \cdot - 4 + 5$

Step 5.1.3

Multiply $- 5$ by $- 4$ .

$- 16 + 20 + 5$

Step 5.2

Simplify by adding numbers.

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Step 5.2.1

Add $- 16$ and $20$ .

$4 + 5$

Step 5.2.2

Add $4$ and $5$ .

$9$