Precalculus Examples

Given that $f (x) = x^{2} - 2 x - 63$ and $g (x) = x + 7$ ; find $(f - g) (x)$ and express the result in standard form.

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(x^{2} - 2 x - 63) - (x + 7)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$x^{2} - 2 x - 63 - x - 1 \cdot 7$

Step 1.2.2

Multiply $- 1$ by $7$ .

$x^{2} - 2 x - 63 - x - 7$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $x$ from $- 2 x$ .

$x^{2} - 3 x - 63 - 7$

Step 1.3.2

Subtract $7$ from $- 63$ .

$x^{2} - 3 x - 70$

Step 2

Evaluate $f - g$ at $x$ .

${(x)}^{2} - 3 x - 70$

Step 3

Simplify ${(x)}^{2} - 3 x - 70$ .

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Step 3.1

Remove parentheses.

${(x)}^{2} - 3 x - 70$

Step 3.2

Remove parentheses.

$x^{2} - 3 x - 70$