Algebra Examples

$y = \sqrt{x - 2}$

Step 1

Rewrite the equation as $\sqrt{x - 2} = y$ .

$\sqrt{x - 2} = y$

Step 2

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

${\sqrt{x - 2}}^{2} = y^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

${(x - 2)}^{1} = y^{2}$

Step 3.2.1.2

Simplify.

$x - 2 = y^{2}$

Step 4

Add $2$ to both sides of the equation.

$x = y^{2} + 2$

Step 5

To rewrite as a function of $y$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

$f (y) = y^{2} + 2$