Solve y=1/2(x^4-1)

$$y = \frac { 1 } { 2 } ( x ^ { 4 } - 1 )$$

Solve for y

$$y=\frac{x^{4}-1}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by x^{4}-1.

$$y=\frac{1}{2}x^{4}-\frac{1}{2}$$

Solve for x (complex solution)

$$x=i\sqrt[4]{2y+1}$$

$$x=\sqrt[4]{2y+1}$$

$$x=-\sqrt[4]{2y+1}$$

$$x=-i\sqrt[4]{2y+1}$$

Solve for x

$$x=\sqrt[4]{2y+1}$$

$$x=-\sqrt[4]{2y+1}\text{, }y\geq -\frac{1}{2}$$