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avatar+702 

Let
f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

 Jul 14, 2024
 #1
avatar+129842 
+1

\(f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}. \)

 

 

x cannot  = 0

 

1 + 3/x  =  [ x + 3] / x

 

2 /  [ ( x + 3) /x ] =   2x / [x + 3]

 

x cannot = -3

 

1 + 2x  / [ x + 3]  =   [ x + 3 + 2x ] / [ x + 3] = [ 3x + 3] / [x + 3]

 

1/ ([3x + 3] /[x + 3]) =    [x + 3] / [ 3x + 3]

 

x cannot = -1

 

 

cool cool cool

 Jul 15, 2024

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