1. The problem statement, all variables and given/known data If g(x) is one-to-one and differentiable at every point in R, then its reciprocal 1/g(x) is also differentiable at every point in its domain. True of False? 2. Relevant equations 3. The attempt at a solution I have tried several times, and the statement seems to be right. I think 1/g(x) can be regarded as 1/u and u=g(x), so 1/g(x) ' = 1/u ' * g'(x)=g'(x)/g(x) (I don't know if this is right...), but I'm stucked here and can't go any further because I don't know how to prove a function to be one-to-one.. I'll be very grateful if anyone can help me.. Thanks!!!