Write as a Function of x x=7y^2+4

$x = 7 y^{2} + 4$

Step 1

Rewrite the equation as $7 y^{2} + 4 = x$ .

$7 y^{2} + 4 = x$

Step 2

Subtract $4$ from both sides of the equation.

$7 y^{2} = x - 4$

Step 3

Divide each term in $7 y^{2} = x - 4$ by $7$ and simplify.

Divide each term in $7 y^{2} = x - 4$ by $7$ .

$\frac{7 y^{2}}{7} = \frac{x}{7} + \frac{- 4}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y^{2}}{7} = \frac{x}{7} + \frac{- 4}{7}$

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

$y^{2} = \frac{x}{7} + \frac{- 4}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$y^{2} = \frac{x}{7} - \frac{4}{7}$

Step 4

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

$y = \pm \sqrt{\frac{x}{7} - \frac{4}{7}}$

Step 5

Simplify $\pm \sqrt{\frac{x}{7} - \frac{4}{7}}$ .

Combine the numerators over the common denominator.

$y = \pm \sqrt{\frac{x - 4}{7}}$

Rewrite $\sqrt{\frac{x - 4}{7}}$ as $\frac{\sqrt{x - 4}}{\sqrt{7}}$ .

$y = \pm \frac{\sqrt{x - 4}}{\sqrt{7}}$

Multiply $\frac{\sqrt{x - 4}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$y = \pm \frac{\sqrt{x - 4}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{x - 4}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Raise $\sqrt{7}$ to the power of $1$ .

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

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

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{{\sqrt{7}}^{2}}$

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

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

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{7^{\frac{2}{2}}}$

Rewrite the expression.

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{7^{1}}$

Evaluate the exponent.

$y = \pm \frac{\sqrt{x - 4} \sqrt{7}}{7}$

Combine using the product rule for radicals.

$y = \pm \frac{\sqrt{(x - 4) \cdot 7}}{7}$

Reorder factors in $\pm \frac{\sqrt{(x - 4) \cdot 7}}{7}$ .

$y = \pm \frac{\sqrt{7 (x - 4)}}{7}$

Step 6

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.

$y = \frac{\sqrt{7 (x - 4)}}{7}$

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

$y = - \frac{\sqrt{7 (x - 4)}}{7}$

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

$y = \frac{\sqrt{7 (x - 4)}}{7}$

$y = - \frac{\sqrt{7 (x - 4)}}{7}$

$y = \frac{\sqrt{7 (x - 4)}}{7}$

$y = - \frac{\sqrt{7 (x - 4)}}{7}$

Step 7

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.

$f (x) = \frac{\sqrt{7 (x - 4)}}{7}, - \frac{\sqrt{7 (x - 4)}}{7}$

Write as a Function of x x=7y^2+4

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