Precalculus Examples

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

Step 1

Evaluate $h - g$ .

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Step 1.1

Replace the function designators in $h - g$ with the actual functions.

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

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4 n + 5 - (3 n) - 1 \cdot 4$

Step 1.2.2

Multiply $3$ by $- 1$ .

$4 n + 5 - 3 n - 1 \cdot 4$

Step 1.2.3

Multiply $- 1$ by $4$ .

$4 n + 5 - 3 n - 4$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $3 n$ from $4 n$ .

$n + 5 - 4$

Step 1.3.2

Subtract $4$ from $5$ .

$n + 1$

Step 2

Evaluate $h - g$ at $n$ .

$(n) + 1$

Step 3

Simplify $(n) + 1$ .

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Step 3.1

Remove parentheses.

$(n) + 1$

Step 3.2

Remove parentheses.

$n + 1$