Question

Which equation is the inverse of (x minus 4) squared minus two-thirds = 6y minus 12?
y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction
y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot
y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot
negative (x minus 4) squared minus two-thirds = negative 6 y + 12

Answer 1

Start with (x − 4)^2 − 2/3 = 6y − 12. Solve for y, then swap x and y:

6y = (x − 4)^2 + 34/3 => y = (1/6)(x − 4)^2 + 17/9.

Swap x and y to get the inverse: x = (1/6)(y − 4)^2 + 17/9
=> (y − 4)^2 = 6x − 34/3
=> y = 4 ± sqrt(6x − 34/3).

So the correct choice is: y = 4 ± √(6x − 34/3).