Write as a Function of x x-y^4=1

$x - y^{4} = 1$

Step 1

Subtract $x$ from both sides of the equation.

$- y^{4} = 1 - x$

Step 2

Divide each term in $- y^{4} = 1 - x$ by $- 1$ and simplify.

Divide each term in $- y^{4} = 1 - x$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y^{4}$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

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

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

$y^{4} = - 1 + x$

Step 3

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

$y = \pm \sqrt[4]{- 1 + x}$

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.

$y = \sqrt[4]{- 1 + x}$

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

$y = - \sqrt[4]{- 1 + x}$

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

$y = \sqrt[4]{- 1 + x}$

$y = - \sqrt[4]{- 1 + x}$

$y = \sqrt[4]{- 1 + x}$

$y = - \sqrt[4]{- 1 + x}$

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.

$f (x) = \sqrt[4]{- 1 + x}, - \sqrt[4]{- 1 + x}$

Write as a Function of x x-y^4=1

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