Precalculus Examples

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

Step 1

Replace the variable $x$ with $- \sqrt{3}$ in the expression.

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

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the product rule to $- \sqrt{3}$ .

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

Step 2.1.2

Raise $- 1$ to the power of $2$ .

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

Step 2.1.3

Multiply ${\sqrt{3}}^{2}$ by $1$ .

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

Step 2.1.4

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 2.1.4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.1.4.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 2.1.4.4

Cancel the common factor of $2$ .

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Step 2.1.4.4.1

Cancel the common factor.

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

Step 2.1.4.4.2

Rewrite the expression.

$f (- \sqrt{3}) = 3 \cdot 3 - 4$

Step 2.1.4.5

Evaluate the exponent.

$f (- \sqrt{3}) = 3 \cdot 3 - 4$

Step 2.1.5

Multiply $3$ by $3$ .

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

Step 2.2

Subtract $4$ from $9$ .

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

Step 2.3

The final answer is $5$ .

$5$

Step 3