Question

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

- + x + 8
+VX+8
2
Oy=
NX
x = x +4
+II

Answer 1

First one

Explanation:

y = 2x² - 8

y + 8 = 2x²

x² = (y + 8)2

x = +/- sqrt[(y + 8)/2]

For inverse, interswitch variables

f^-1(x) = +/- sqrt[(x + 8)/2]

Answer 2

A y = ±sqrt((x+8)/2)

Explanation:

y = 2x^2 -8

Exchange x and y

x = 2y^2 -8

Solve for y

Add 8 to each side

x+8 = 2y^2 -8+8

x+8 = 2y^2

Divide each side by 2

(x+8)/2 = 2y^2/2

(x+8)/2 = y^2

Take the square root of each side

±sqrt((x+8)/2) = sqrt(y^2)

±sqrt((x+8)/2) = y