Write as a Function of x x^2-y^2=1

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

Subtract $x^{2}$ from both sides of the equation.

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

Divide each term in $- y^{2} = 1 - x^{2}$ by $- 1$ and simplify.

Divide each term in $- y^{2} = 1 - x^{2}$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

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

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

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

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

Dividing two negative values results in a positive value.

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

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

$y^{2} = - 1 + x^{2}$

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

$y = \pm \sqrt{- 1 + x^{2}}$

Simplify $\pm \sqrt{- 1 + x^{2}}$ .

Simplify the expression.

Rewrite $1$ as $1^{2}$ .

$y = \pm \sqrt{- 1^{2} + x^{2}}$

Reorder $- 1^{2}$ and $x^{2}$ .

$y = \pm \sqrt{x^{2} - 1^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

$y = \pm \sqrt{(x + 1) (x - 1)}$

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.

$y = \sqrt{(x + 1) (x - 1)}$

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

$y = - \sqrt{(x + 1) (x - 1)}$

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

$y = \sqrt{(x + 1) (x - 1)}$

$y = - \sqrt{(x + 1) (x - 1)}$

$y = \sqrt{(x + 1) (x - 1)}$

$y = - \sqrt{(x + 1) (x - 1)}$

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.

$f (x) = \sqrt{(x + 1) (x - 1)}, - \sqrt{(x + 1) (x - 1)}$

Write as a Function of x x^2-y^2=1

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