Precalculus Examples

Given that $f (x) = x^{2} - 13 x + 36$ and $g (x) = x - 9$ ; find $(f - g) (x)$ and express the result in standard form.

Step 1

Evaluate $f - g$ .

Tap for more steps...

Step 1.1

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

$(x^{2} - 13 x + 36) - (x - 9)$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$x^{2} - 13 x + 36 - x - - 9$

Step 1.2.2

Multiply $- 1$ by $- 9$ .

$x^{2} - 13 x + 36 - x + 9$

Step 1.3

Simplify by adding terms.

Tap for more steps...

Step 1.3.1

Subtract $x$ from $- 13 x$ .

$x^{2} - 14 x + 36 + 9$

Step 1.3.2

Add $36$ and $9$ .

$x^{2} - 14 x + 45$

Step 2

Evaluate $f - g$ at $x$ .

${(x)}^{2} - 14 x + 45$

Step 3

Simplify ${(x)}^{2} - 14 x + 45$ .

Tap for more steps...

Step 3.1

Remove parentheses.

${(x)}^{2} - 14 x + 45$

Step 3.2

Remove parentheses.

$x^{2} - 14 x + 45$