+0  
 
-1
54
2
avatar+194 

There are three real numbers $x$ that are not in the domain of

$$f(x) = \frac{1}{1+\frac{1}{1+\frac 1x}}.$$

What is the sum of those three numbers?

 Feb 5, 2021
 #2
avatar+112513 
+1

Well we cannot divide by 0 so

 

\(x\ne0\)

 

 

\(1+\frac{1}{x}\ne0\\ \frac{1}{x}\ne-1\\ x\ne-1 \)

 

 

\(1+\frac{1}{1+\frac{1}{x}}\ne0\\ \frac{1}{1+\frac{1}{x}}\ne-1\\ \frac{x}{x+1}\ne-1\\ x\ne -x-1\\ 2x\ne-1\\ x\ne -\frac{1}{2}\)

 Feb 5, 2021

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