Answer:
[tex]y = \sqrt{\frac{x+8}{2}}[/tex]
Step-by-step explanation:
Here, the given equation,
[tex]y=2x^2-8[/tex]
For finding the inverse, interchange x and y,
[tex]x=2y^2-8[/tex]
Add 8 on both sides,
[tex]x+8=2y^2[/tex]
Divide both sides by 2,
[tex]\frac{x+8}{2}=y^2[/tex]
Taking square root on both sides,
[tex]\sqrt{\frac{x+8}{2}}=y[/tex]
[tex]\implies y = \sqrt{\frac{x+8}{2}}[/tex]
Which is the required inverse of the given equation.
