Inverse of the function

Question

Find the inverse of the given function?

y=f(x)=x^2-3x

Answer 1

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)