Finite Math Examples

$f (- 3) = \frac{\sqrt{x - 3}}{x^{2} - 4}$

Step 1

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = \frac{\sqrt{(- 3) - 3}}{{(- 3)}^{2} - 4}$

Step 2

Simplify the result.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Subtract $3$ from $- 3$ .

$f (- 3) = \frac{\sqrt{- 6}}{{(- 3)}^{2} - 4}$

Step 2.1.2

Rewrite $- 6$ as $- 1 (6)$ .

$f (- 3) = \frac{\sqrt{- 1 \cdot 6}}{{(- 3)}^{2} - 4}$

Step 2.1.3

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$f (- 3) = \frac{\sqrt{- 1} \cdot \sqrt{6}}{{(- 3)}^{2} - 4}$

Step 2.1.4

Rewrite $\sqrt{- 1}$ as $i$ .

$f (- 3) = \frac{i \sqrt{6}}{{(- 3)}^{2} - 4}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Raise $- 3$ to the power of $2$ .

$f (- 3) = \frac{i \sqrt{6}}{9 - 4}$

Step 2.2.2

Subtract $4$ from $9$ .

$f (- 3) = \frac{i \sqrt{6}}{5}$

Step 2.3

The final answer is $\frac{i \sqrt{6}}{5}$ .

$\frac{i \sqrt{6}}{5}$

Step 3