Question

Which equation is the inverse of y = 2x2 – 8?​

Answer 1

The inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$

Explanation:

To find the inverse of the equation $y=2x^{2} -8$, we need to interchange the variables x and y for the variables y and x.

Thus, the equation becomes

$x=2y^{2} -8$

Now, we shall find the value of y.

Now, adding 8 to both sides of the equation, we have,

$x+8=2y^{2}$

Interchanging the sides,

$2y^{2} =x+8$

Dividing by 2 on both sides,

$y^{2} =\frac{x+8}{2}$

Taking square root on both sides,

$y=\pm \sqrt{\frac{x+8}{2}}$

Thus, the inverse of the function is $y=\pm \sqrt{\frac{x+8}{2}}$