Precalculus Examples

$f (\sqrt{2}) = 6 x^{2} + 3 x - 12$

Step 1

Replace the variable $x$ with $\sqrt{2}$ in the expression.

$f (\sqrt{2}) = 6 {(\sqrt{2})}^{2} + 3 (\sqrt{2}) - 12$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

$f (\sqrt{2}) = 6 {(2^{\frac{1}{2}})}^{2} + 3 (\sqrt{2}) - 12$

Step 2.1.1.2

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

$f (\sqrt{2}) = 6 \cdot 2^{\frac{1}{2} \cdot 2} + 3 (\sqrt{2}) - 12$

Step 2.1.1.3

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

$f (\sqrt{2}) = 6 \cdot 2^{\frac{2}{2}} + 3 (\sqrt{2}) - 12$

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Cancel the common factor.

$f (\sqrt{2}) = 6 \cdot 2^{\frac{2}{2}} + 3 (\sqrt{2}) - 12$

Step 2.1.1.4.2

Rewrite the expression.

$f (\sqrt{2}) = 6 \cdot 2 + 3 (\sqrt{2}) - 12$

Step 2.1.1.5

Evaluate the exponent.

$f (\sqrt{2}) = 6 \cdot 2 + 3 (\sqrt{2}) - 12$

Step 2.1.2

Multiply $6$ by $2$ .

$f (\sqrt{2}) = 12 + 3 \sqrt{2} - 12$

Step 2.2

Simplify by subtracting numbers.

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Step 2.2.1

Subtract $12$ from $12$ .

$f (\sqrt{2}) = 0 + 3 \sqrt{2}$

Step 2.2.2

Add $0$ and $3 \sqrt{2}$ .

$f (\sqrt{2}) = 3 \sqrt{2}$

Step 2.3

The final answer is $3 \sqrt{2}$ .

$3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

Step 4