Precalculus Examples

$g (x) = 2 x - 5$ $h (x) = 4 x + 5$ Find $g (3) - h (3)$

Step 1

Replace the variable $x$ with $3$ in the expression.

$g (3) = 2 (3) - 5$

Step 2

Replace the variable $x$ with $3$ in the expression.

$h (3) = 4 (3) + 5$

Step 3

Replace the function designators in $g (3) - h \cdot 3$ with the actual functions.

$(2 (3) - 5) - (4 (3) + 5)$

Step 4

Simplify $(2 (3) - 5) - (4 (3) + 5)$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $2$ by $3$ .

$6 - 5 - (4 (3) + 5)$

Step 4.1.2

Multiply $4$ by $3$ .

$6 - 5 - (12 + 5)$

Step 4.1.3

Add $12$ and $5$ .

$6 - 5 - 1 \cdot 17$

Step 4.1.4

Multiply $- 1$ by $17$ .

$6 - 5 - 17$

Step 4.2

Simplify by subtracting numbers.

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Step 4.2.1

Subtract $5$ from $6$ .

$1 - 17$

Step 4.2.2

Subtract $17$ from $1$ .

$- 16$