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 $a+d$?)

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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 $a+d$?

Guest Aug 5, 2022

edited by Guest Aug 5, 2022

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Guest Aug 5, 2022

Guest · Answer 1 · 2022-08-05T09:41:14

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.