Question

Which equation is the inverse of y = 9x2 – 4?
y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction
y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot
y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction
y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds

Answer 1

Swap x and y and solve: x = 9y^2 - 4
=> x + 4 = 9y^2
=> y^2 = (x + 4)/9
=> y = ± sqrt((x + 4)/9) = ± (sqrt(x + 4))/3.

That matches choice 3: y = (± sqrt(x + 4)) / 3 (with domain x ≥ -4).