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Let f(x) = (x - 1)/(x + 1). Compute f(f(f(5))).

 Jun 17, 2022
 #1
avatar+578 
+1

 

\(f(f(f(5)))=\)\(\frac{\left(\frac{\left(\frac{\left(x-1\right)}{\left(x+1\right)}-1\right)}{\left(\frac{\left(x-1\right)}{\left(x+1\right)}+1\right)}-1\right)}{\left(\frac{\left(\frac{\left(x-1\right)}{\left(x+1\right)}-1\right)}{\left(\frac{\left(x-1\right)}{\left(x+1\right)}+1\right)}+1\right)}\)

 

That simplifies to \(\frac{-x-1}{x-1}\)

 

Substituting 5 gives \(\frac{-\left(5\right)-1}{\left(5\right)-1}\)

 

=\(-3/2\)

 Jun 18, 2022
 #2
avatar+117746 
+1

Just do it one bit at a time.

Let f(x) = (x - 1)/(x + 1). Compute f(f(f(5))).

 

f(5)=(5 - 1)/(5 + 1) = 4/6  =  2/3

 

\(f(f(5)) = f(\frac{2}{3}) \\ =\frac{ (\frac{2}{3}-1) }{ (\frac{2}{3}+1) }\\~\\ =\frac{ \frac{-1}{3} }{ \frac{5}{3} }\\~\\ =\frac{-1}{5}\\~\\ f(f(f(5)) )=f( f(\frac{2}{3}))=f(\frac{-1}{5}) \\ etc\)

 

 

you need to check what i have done and then finish it.

 Jun 18, 2022

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