Find the Inverse y=7x^2-10

$y = 7 x^{2} - 10$

Interchange the variables.

$x = 7 y^{2} - 10$

Solve for $y$ .

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Rewrite the equation as $7 y^{2} - 10 = x$ .

$7 y^{2} - 10 = x$

Add $10$ to both sides of the equation.

$7 y^{2} = x + 10$

Divide each term by $7$ and simplify.

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Divide each term in $7 y^{2} = x + 10$ by $7$ .

$\frac{7 y^{2}}{7} = \frac{x}{7} + \frac{10}{7}$

Cancel the common factor of $7$ .

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Cancel the common factor.

$\frac{7 y^{2}}{7} = \frac{x}{7} + \frac{10}{7}$

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

$y^{2} = \frac{x}{7} + \frac{10}{7}$

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

$y = \pm \sqrt{\frac{x}{7} + \frac{10}{7}}$

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

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Simplify the right side of the equation.

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Combine the numerators over the common denominator.

$y = \pm \sqrt{\frac{x + 10}{7}}$

Rewrite $\sqrt{\frac{x + 10}{7}}$ as $\frac{\sqrt{x + 10}}{\sqrt{7}}$ .

$y = \pm \frac{\sqrt{x + 10}}{\sqrt{7}}$

Multiply $\frac{\sqrt{x + 10}}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$y = \pm \frac{\sqrt{x + 10}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Combine and simplify the denominator.

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Multiply $\frac{\sqrt{x + 10}}{\sqrt{7}}$ and $\frac{\sqrt{7}}{\sqrt{7}}$ .

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

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

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

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

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

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

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Add $1$ and $1$ .

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{{\sqrt{7}}^{2}}$

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

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

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

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

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

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

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{7^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{7^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{7}$

Evaluate the exponent.

$y = \pm \frac{\sqrt{x + 10} \sqrt{7}}{7}$

Combine using the product rule for radicals.

$y = \pm \frac{\sqrt{(x + 10) \cdot 7}}{7}$

Reorder factors in $\pm \frac{\sqrt{(x + 10) \cdot 7}}{7}$ .

$y = \pm \frac{\sqrt{7 (x + 10)}}{7}$

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

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