SOLUTION: f(x)=(5)/(x+4), g(x)=(1)/(x) find (f o g)(x) and the domain of f o g
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Question 412525: f(x)=(5)/(x+4), g(x)=(1)/(x) find (f o g)(x) and the domain of f o g
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
(x)\ =\ f\left(g(x)\right))
(x)\ =\ \frac{5}{\frac{1}{x}\,+\,4}\ =\ \frac{5}{\frac{1\,+\,4}{x}}\ =\ \frac{5x}{1\,+\,4x})
First find the domain of the "inside" function:
\right)\ =\ \{x\,|\,x\ \in\ \mathbb{R},\ x\ \neq\ 0\})
Then find the domain of the simplified composite:
\ =\ \{x\,|\,x\ \in\ \mathbb{R},\ x\ \neq\ -\frac{1}{4}\})
And combine:
(x)\right)\ =\ \{x\,|\,x\ \in\ \mathbb{R},\ x\ \neq\ -\frac{1}{4},\ x\ \neq\ 0\})
John
My calculator said it, I believe it, that settles it
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