Precalculus Examples

Given that $f (x) = x^{2} - 4 x - 21$ and $g (x) = x - 7$ ; find $f (x) - g (x)$ and express the result in standard form.

Step 1

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

$(x^{2} - 4 x - 21) - (x - 7)$

Step 2

Simplify $(x^{2} - 4 x - 21) - (x - 7)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x^{2} - 4 x - 21 - x - - 7$

Step 2.1.2

Multiply $- 1$ by $- 7$ .

$x^{2} - 4 x - 21 - x + 7$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x$ from $- 4 x$ .

$x^{2} - 5 x - 21 + 7$

Step 2.2.2

Add $- 21$ and $7$ .

$x^{2} - 5 x - 14$