Answer:
f^-1(x) = √((y +9)/3)
Explanation:
You want the inverse function of y = 3x² -9.
Inverse function
The given relation will only have an inverse function if its domain is restricted to values x ≥ 0.
We can find that inverse function by interchanging the variables x and y, then solving for y:
x = 3y² -9
x +9 = 3y² . . . . . . . add 9
(x +9)/3 = y² . . . . . . divide by 3
y = √((x+9)/3) . . . . . take the square root
The inverse function is f^-1(x) = √((x +9)/3).