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(If $f(x)=\frac{ax+b}{cx+d}, abcd\not=0$ and\(f(f(x))=x\) for all $x$ in the domain of $f$, what is the value of $a+d$?)

 

Thanks! (In LaTeX:)

 

If\(f(x)=\frac{ax+b}{cx+d}, abcd\not=0\) and \(f(f(x))=x\) for all \(x\) in the domain of \(f\), what is the value of \(a+d\)?

 
 Aug 5, 2022
edited by Guest  Aug 5, 2022
 #1
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f(f(x)) = (a*(ax + b)/(cx + d) + b)/(c*(ax + b)/(cx + d) + d) = x

 

Simplying and comparing coefficients gives us a + d = -1.

 
 Aug 5, 2022
 #3
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The awnser was 0, thanks though!

 
Guest Aug 5, 2022
 #2
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Thanks!

 
 Aug 5, 2022

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