Precalculus Examples

If $f (x) = \sqrt{x} + 12$ and $g (x) = 2 \sqrt{x}$ ; what is the value of $(f - g) (144)$ ?

Step 1

Evaluate $f - g$ .

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Step 1.1

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

$(\sqrt{x} + 12) - (2 \sqrt{x})$

Step 1.2

Multiply $2$ by $- 1$ .

$\sqrt{x} + 12 - 2 \sqrt{x}$

Step 1.3

Subtract $2 \sqrt{x}$ from $\sqrt{x}$ .

$12 - \sqrt{x}$

Step 2

Evaluate $f - g$ at $144$ .

$12 - \sqrt{144}$

Step 3

Simplify $12 - \sqrt{144}$ .

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Step 3.1

Remove parentheses.

$12 - \sqrt{144}$

Step 3.2

Simplify each term.

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Step 3.2.1

Rewrite $144$ as $12^{2}$ .

$12 - \sqrt{12^{2}}$

Step 3.2.2

Pull terms out from under the radical, assuming positive real numbers.

$12 - 1 \cdot 12$

Step 3.2.3

Multiply $- 1$ by $12$ .

$12 - 12$

Step 3.3

Subtract $12$ from $12$ .

$0$