Calculus Examples

$f (x) = - 3 x$ , $g (x) = - 5 - \frac{5 x}{2}$ , $(g \circ f)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

$g (- 3 x) = - 5 - \frac{5 (- 3 x)}{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $- 3$ by $5$ .

$g (- 3 x) = - 5 - \frac{- 15 x}{2}$

Step 3.2

Move the negative in front of the fraction.

$g (- 3 x) = - 5 + \frac{15 x}{2}$

Step 3.3

Multiply $- - \frac{15 x}{2}$ .

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Step 3.3.1

Multiply $- 1$ by $- 1$ .

$g (- 3 x) = - 5 + 1 (\frac{15 x}{2})$

Step 3.3.2

Multiply $\frac{15 x}{2}$ by $1$ .

$g (- 3 x) = - 5 + \frac{15 x}{2}$

Step 4

Reorder $- 5$ and $\frac{15 x}{2}$ .

$g (- 3 x) = \frac{15 x}{2} - 5$