What is the inverse of y=9x^2-4

You have y in terms of x. Solve for x in terms of y.

y = 9x^2 - 4

Add 4 to both sides:

y + 4 = 9x^2

Divide both sides by 9:

(y+4) * (1/9) = x^2

Take the square root of both sides:

(y+4) ^ (1/2) * (1/9) ^ (1/2) = x

(y+4) ^ (1/2) * 1/3 = x

x = 1/3 (y+4) ^ (1/2)