Algebra Examples

$f (x) = - 3 x$ , $g (x) = | x - 1 |$ , $(f \cdot g) (- 3)$

Step 1

Evaluate $f \cdot g$ .

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Step 1.1

Replace the function designators in $f \cdot g$ with the actual functions.

$(- 3 x) \cdot (| x - 1 |)$

Step 1.2

Reorder factors in $- 3 x (| x - 1 |)$ .

$- 3 x | x - 1 |$

Step 2

Evaluate $f \cdot g$ at $- 3$ .

$- 3 \cdot - 3 | (- 3) - 1 |$

Step 3

Simplify $- 3 \cdot - 3 | (- 3) - 1 |$ .

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Step 3.1

Remove parentheses.

$- 3 \cdot - 3 | (- 3) - 1 |$

Step 3.2

Multiply $- 3$ by $- 3$ .

$9 | (- 3) - 1 |$

Step 3.3

Subtract $1$ from $- 3$ .

$9 | - 4 |$

Step 3.4

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$9 \cdot 4$

Step 3.5

Multiply $9$ by $4$ .

$36$