Write as a Function of x x=5y^2

$x = 5 y^{2}$

Rewrite the equation as $5 y^{2} = x$ .

$5 y^{2} = x$

Divide each term in $5 y^{2} = x$ by $5$ and simplify.

Divide each term in $5 y^{2} = x$ by $5$ .

$\frac{5 y^{2}}{5} = \frac{x}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y^{2}}{5} = \frac{x}{5}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{x}{5}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{\frac{x}{5}}$

Simplify $\pm \sqrt{\frac{x}{5}}$ .

Rewrite $\sqrt{\frac{x}{5}}$ as $\frac{\sqrt{x}}{\sqrt{5}}$ .

$y = \pm \frac{\sqrt{x}}{\sqrt{5}}$

Multiply $\frac{\sqrt{x}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$y = \pm \frac{\sqrt{x}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$y = \pm \frac{\sqrt{x} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$y = \pm \frac{\sqrt{x} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$y = \pm \frac{\sqrt{x} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \pm \frac{\sqrt{x} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$y = \pm \frac{\sqrt{x} \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$y = \pm \frac{\sqrt{x} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$y = \pm \frac{\sqrt{x} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$y = \pm \frac{\sqrt{x} \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = \pm \frac{\sqrt{x} \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$y = \pm \frac{\sqrt{x} \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$y = \pm \frac{\sqrt{x} \sqrt{5}}{5}$

Combine using the product rule for radicals.

$y = \pm \frac{\sqrt{x \cdot 5}}{5}$

Reorder factors in $\pm \frac{\sqrt{x \cdot 5}}{5}$ .

$y = \pm \frac{\sqrt{5 x}}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{\sqrt{5 x}}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{\sqrt{5 x}}{5}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{\sqrt{5 x}}{5}$

$y = - \frac{\sqrt{5 x}}{5}$

$y = \frac{\sqrt{5 x}}{5}$

$y = - \frac{\sqrt{5 x}}{5}$

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

$f (x) = \frac{\sqrt{5 x}}{5}, - \frac{\sqrt{5 x}}{5}$

Write as a Function of x x=5y^2

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