Question 1173271
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Your definition of *[tex \Large f(x)] is ambiguous.  There is no way to tell if you meant *[tex \Large f(x)\ =\ \frac{1}{\log(x)\,+\,1}] or *[tex \Large f(x)\ =\ \frac{1}{\log(x)}\ +\ 1].  Just using *[tex \Large \log] without specifying the base is also ambiguous because to some it means *[tex \Large \ln(x)] and to some it means *[tex \Large \log_{10}]


The domain of *[tex \Large g] is all reals and the range of *[tex \Large g] is the closed interval from -1 to 1.  The domain of the *[tex \Large \log] function is all positive reals, which means that you must restrict the range of *[tex \Large g] to the interval (0,1] for the composite function, which means that you must restrict the domain of *[tex \Large g] to the interval *[tex \Large 0\,+\,2n\pi\ <\ x\ \leq\ \pi\,+\,2n\pi] where *[tex \Large n\ \in\ \mathbb{Z}].  Then depending on which of the definitions of *[tex \Large f] you meant, you must either restrict the range of *[tex \Large \log(x)] such that the denominator in *[tex \Large f] is not equal to zero, so either *[tex \Large \log(sin(x))\ \not =\ -1] or *[tex \Large \log(sin(x))\ \not =\ \frac{1}{b}] where *[tex \Large b] is the log base you meant.


																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
*[illustration darwinfish.jpg]

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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