f(x)=2x/(x^2+6) for x>=b (b is a real number)
1. Find f'(x)
2. Hence find the smallest exact value of b for which the inverse function f^(-1) exists.
My question is: isn't b arbitrary? Couldn't I just pick any real number and then the domain of the inverse would just be x>f(b) since the domain and range switch between inverses. Except I couldn't pick an imaginary number, which curiously is also the domain restriction of f(x) and f'(x) i.e. sqrt(-6). Also, what is the purpose of finding the derivative?

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