Write as a Function of x 16+y^2=x^2

$16 + y^{2} = x^{2}$

Step 1

Subtract $16$ from both sides of the equation.

$y^{2} = x^{2} - 16$

Step 2

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

$y = \pm \sqrt{x^{2} - 16}$

Step 3

Simplify $\pm \sqrt{x^{2} - 16}$ .

Rewrite $16$ as $4^{2}$ .

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

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 $b = 4$ .

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

Step 4

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.

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

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

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

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

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

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

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

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

Step 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.

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

Write as a Function of x 16+y^2=x^2

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