Finite Math Examples

$f (x) = - x^{2} - 4 x - 3$ , $g (x) = - 3 x$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (- 3 x)$ by substituting in the value of $g$ into $f$ .

$f (- 3 x) = - {(- 3 x)}^{2} - 4 (- 3 x) - 3$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $- 3 x$ .

$f (- 3 x) = - ({(- 3)}^{2} x^{2}) - 4 (- 3 x) - 3$

Step 3.2

Raise $- 3$ to the power of $2$ .

$f (- 3 x) = - (9 x^{2}) - 4 (- 3 x) - 3$

Step 3.3

Multiply $9$ by $- 1$ .

$f (- 3 x) = - 9 x^{2} - 4 (- 3 x) - 3$

Step 3.4

Multiply $- 3$ by $- 4$ .

$f (- 3 x) = - 9 x^{2} + 12 x - 3$