SOLUTION: 6. a) Given f(x) = log(x) and g(x) = 1/(𝑥+3), identify the steps you would take to determine the domain of (f ∘ g)(x). What is the domain of (f ∘ g)(x)?
b) Would the dom
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Question 1162522: 6. a) Given f(x) = log(x) and g(x) = 1/(𝑥+3), identify the steps you would take to determine the domain of (f ∘ g)(x). What is the domain of (f ∘ g)(x)?
b) Would the domain of (g ∘ f)(x) be the same? Explain. What is the domain of (g ∘ f)(x)?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
(x)\ =\ f\(g(x)\)\ =\ \log\(g(x)\)\ =\ \log\(\frac{1}{x\,+\,3}\))
Since the domain of the log function is 
, then
Hence
Therefore
\ =\ \{x\,\in\,\mathbb{R}\,|\,x\,>\,-3\})
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(x)\ =\ g\(f(x)\)\ =\ \frac{1}{f(x)\,+\,3}\ =\ \frac{1}{\log(x)\,+\,3})
Since rational functions are not defined for any value of the independent variable that causes the denominator of the function to equal zero,
\,+\,3\ \neq\ 0)
\ \neq\ -3)
So, depending on whether you mean 
or 
when you write 
without specifying the base,
\ =\ \{x\,\in\,\mathbb{R}\,|\,x\,\neq\,10^{-3}\})
or
\ =\ \{x\,\in\,\mathbb{R}\,|\,x\,\neq\,e^{-3}\})
John
My calculator said it, I believe it, that settles it
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