Let f(x) = 2x2-3, x > 3
I am not sure about your problem, is it f(x) = 2x^2 -3 ? I guess so. If so, to me, you set y = 2x^2 -3 and then to find the inverse function, you just switch the variables and turn it into x = 2y^2 -3 . then solve for y. the new y is inverse function of f(x) . x= 1y^2 -3 —> 2y^2 = x+3 —> y^2 = (x+3)/2 --> y = ± sqrt ((x+3)/2) . that is your inverse function.
take derivative is not a hard problem, do as usual