Determine the equation of the inverse function if f(x) = 2x^2+3, and x≥0.

Question

The answer is supposed to be f^-1(x)=[√(2x-6)]/2.

This is what I did:

x=2y^2+3
2y^2=x-3
y^2=(x-3)/2
y=√[(x-3)/2]

Did I do something wrong?

Thanks!

Answer 1

I think you did it correctly.

Of course the domain is limited because the answer is imaginary if x <3

Answer 2

the answers are the same

√[(x-3)/2] = √[(x-3)/2 * 2/2] = √(2x-6)/2