Find the Domain x=y^6

$x = y^{6}$

Step 1

Rewrite the equation as $y^{6} = x$ .

$y^{6} = x$

Step 2

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

$y = \pm \sqrt[6]{x}$

Step 3

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.

$y = \sqrt[6]{x}$

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

$y = - \sqrt[6]{x}$

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

$y = \sqrt[6]{x}$

$y = - \sqrt[6]{x}$

$y = \sqrt[6]{x}$

$y = - \sqrt[6]{x}$

Step 4

Set the radicand in $\sqrt[6]{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 6