Write as a Function of x y^4=3x^2+2x

$y^{4} = 3 x^{2} + 2 x$

Step 1

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

$y = \pm \sqrt[4]{3 x^{2} + 2 x}$

Step 2

Factor $x$ out of $3 x^{2} + 2 x$ .

Factor $x$ out of $3 x^{2}$ .

$y = \pm \sqrt[4]{x (3 x) + 2 x}$

Factor $x$ out of $2 x$ .

$y = \pm \sqrt[4]{x (3 x) + x \cdot 2}$

Factor $x$ out of $x (3 x) + x \cdot 2$ .

$y = \pm \sqrt[4]{x (3 x + 2)}$

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.

$y = \sqrt[4]{x (3 x + 2)}$

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

$y = - \sqrt[4]{x (3 x + 2)}$

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

$y = \sqrt[4]{x (3 x + 2)}$

$y = - \sqrt[4]{x (3 x + 2)}$

$y = \sqrt[4]{x (3 x + 2)}$

$y = - \sqrt[4]{x (3 x + 2)}$

Step 4

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.

$f (x) = \sqrt[4]{x (3 x + 2)}, - \sqrt[4]{x (3 x + 2)}$

Write as a Function of x y^4=3x^2+2x

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