can someone help me with these true or false questions? True/False. There exists

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can someone help me with these true or false questions?


True/False. There exists a non-constant function f such that (f(x))^2=x^2. If your answer is true, then give all of the functions that satisfy this condition. If the answer is false, explain.


True/False. If f(x)g(x)=x, then it is possible that f and g are differentiable and f(0)=g(0)=0. If you answered true, then explain your reasoning. If you answered false, then give a counterexample.



True/False. If f is integrable on [a,b], then there exists a number x in the open interval (a,b) such that
?_a^x f=?_x^bf
If your answer is true, then explain your reasoning. If you chose false, then give a counterexample.

Explanation / Answer

you can find similar questions here. hope this link helpful. http://www.mathdb.org/notes_download/elementary/algebra/ae_A1.pdf

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