Respuesta :
Answer:
y = plus-or-minus StartRoot StartFraction x + 8 Over 2 EndFraction EndRoot
[tex]y=\pm\sqrt{\frac{x+8}{2}}[/tex]
Step-by-step explanation:
Given:
The equation to find inverse is given as:
[tex]y=2x^2-8[/tex]
In order to find the inverse, we apply the following steps.
Step 1: Switch 'y' with 'x' and 'x' with 'y'. Thi gives,
[tex]x=2y^2-8[/tex]
Step 2: Now, again rewrite the above equation in terms of 'y'.
Adding 8 on both sides, we get:
[tex]x+8=2y^2-8+8[/tex]
[tex]x+8=2y^2[/tex]
Now, rewriting 'y' terms on the left side of the equation, we get
[tex]2y^2=x+8[/tex]
Dividing both sides by 2, we get:
[tex]\frac{2y^2}{2}=\frac{x+8}{2}\\\\y^2=\frac{x+8}{2}[/tex]
Taking square root on both sides, we get:
[tex]\sqrt{y^2}=\pm\sqrt{\frac{x+8}{2}}\\\\y=\pm\sqrt{\frac{x+8}{2}}[/tex]
Thus, the inverse of the given equation is [tex]y=\pm\sqrt{\frac{x+8}{2}}[/tex].
So, the first option is correct.
