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

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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

### 3+0 Answers

#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