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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?

 Nov 11, 2014

Best Answer 

 #1
avatar+118723 
+10

Well you cannot divide by 0 so 0 is one of the numbers.

1+1/x can also not equal zero so x cannot be -1

 

Also if you simplify this down you get to a point where  

$$f(x)=\frac{1}{\frac{2x+1}{x+1}}$$

 

You cant divide by 0 so  2x+1 not eqal 0

x not equal -1/2

 

So the domain does not include  0,-1/2 or -1

the sum of these is -3/2

 

I have not checked any of my working. :)

 Nov 11, 2014
 #1
avatar+118723 
+10
Best Answer

Well you cannot divide by 0 so 0 is one of the numbers.

1+1/x can also not equal zero so x cannot be -1

 

Also if you simplify this down you get to a point where  

$$f(x)=\frac{1}{\frac{2x+1}{x+1}}$$

 

You cant divide by 0 so  2x+1 not eqal 0

x not equal -1/2

 

So the domain does not include  0,-1/2 or -1

the sum of these is -3/2

 

I have not checked any of my working. :)

Melody Nov 11, 2014

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