y=x²-3x
we have y in terms of x, and need to get x in terms of y
completing the square x²-3x = (x-3/2)² - (3/2)²
so, y =(x-3/2)²-9/4
y+9/4= (x-3/2)²
(x-3/2)²=y+9/4
Taking the square root of both sides we obtain
x-3/2=sqrt(y+9/4) (square root can be positive or negative.I'm assuming it's positive here)
x=3/2+sqrt(y+9/4)
The inverse of f(x) =3/2+sqrt(x+9/4)