SOLUTION: Let f(x) = 1/logx + 1 and g(x) = sin x.
Determine the domain and range for the composite function
y = f(g(x)). Explain how you found the domain and range. Unjustified domains and
Algebra.Com
Question 1173271: Let f(x) = 1/logx + 1 and g(x) = sin x.
Determine the domain and range for the composite function
y = f(g(x)). Explain how you found the domain and range. Unjustified domains and ranges will receive zero marks.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Your definition of )
is ambiguous. There is no way to tell if you meant \ =\ \frac{1}{\log(x)\,+\,1})
or \ =\ \frac{1}{\log(x)}\ +\ 1)
. Just using 
without specifying the base is also ambiguous because to some it means )
and to some it means 
The domain of 
is all reals and the range of is the closed interval from -1 to 1. The domain of the function is all positive reals, which means that you must restrict the range of to the interval (0,1] for the composite function, which means that you must restrict the domain of to the interval 
where 
. Then depending on which of the definitions of 
you meant, you must either restrict the range of )
such that the denominator in is not equal to zero, so either )\ \not =\ -1)
or )\ \not =\ \frac{1}{b})
where 
is the log base you meant.
John
My calculator said it, I believe it, that settles it
From
I > Ø
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