Finite Math Examples

$f (x) = \sqrt{6 - x}$

Step 1

Set $\sqrt{6 - x}$ equal to $0$ .

$\sqrt{6 - x} = 0$

Step 2

Solve for $x$ .

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Step 2.1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{6 - x}}^{2} = 0^{2}$

Step 2.2

Simplify each side of the equation.

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Step 2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 - x}$ as ${(6 - x)}^{\frac{1}{2}}$ .

${({(6 - x)}^{\frac{1}{2}})}^{2} = 0^{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Simplify ${({(6 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.1.1

Multiply the exponents in ${({(6 - x)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.2.1.1.1

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

${(6 - x)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 2.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.2.1.1.2.1

Cancel the common factor.

${(6 - x)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 2.2.2.1.1.2.2

Rewrite the expression.

${(6 - x)}^{1} = 0^{2}$

Step 2.2.2.1.2

Simplify.

$6 - x = 0^{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Raising $0$ to any positive power yields $0$ .

$6 - x = 0$

Step 2.3

Solve for $x$ .

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Step 2.3.1

Subtract $6$ from both sides of the equation.

$- x = - 6$

Step 2.3.2

Divide each term in $- x = - 6$ by $- 1$ and simplify.

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Step 2.3.2.1

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Step 2.3.2.2

Simplify the left side.

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Step 2.3.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Step 2.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Step 2.3.2.3

Simplify the right side.

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Step 2.3.2.3.1

Divide $- 6$ by $- 1$ .

$x = 6$

Step 3