I have two questions for you:
1. What is the domain of f(x)?
2. What is the derivative of f(x)?
I would agree with all but your last line of the computation. h never actually equals zero (it's a limit!), whereas the numerator is identically zero. Hence the overall limit is what?
I was asking about the domain of f(x), in case the problem had artificially restricted the domain. But no, you have the natural domain (the largest domain that makes sense). So, based on that information, plus the corrected derivative, can you tell me what the domain of the derivative is?
I agree; this is what I was getting at in post # 4, and what I was trying to get the OP'er to figure out on her own.
"Excite and direct the self-activities of the pupil, and as a rule tell him nothing that he can learn himself." - Law # 6 from John Milton Gregory's The Seven Laws of Teaching.