+1791 The function
f(x) = \frac{cx}{4x - 5 - 2x + 8}
satisfies f(f(x))=x for all real numbers x\neq -\frac{3}{2}. Find c.
+266 Please take the time to put your answer in Latex. It helps a lot.
\(f(x) = \frac{cx}{4x - 5 - 2x + 8}\)
\( x\neq -\frac{3}{2}\)
Im going to try and brute force it, but its going to be really ugly.
\(f(f(x)) = \frac{c(\frac{cx}{4x - 5 - 2x + 8})}{4(\frac{cx}{4x - 5 - 2x + 8}) - 5 - 2(\frac{cx}{4x - 5 - 2x + 8}) + 8}\)
\(f(f(x)) = \frac{c(\frac{cx}{4x - 5 - 2x + 8})}{2(\frac{cx}{4x - 5 - 2x + 8}) +3}\)
\(x = {\frac{c^2x}{2x+3}}\cdot{\frac{2x+3}{2cx+6x+9} }\)
\(x = {\frac{c^2x}{2cx+6x+9} }\)
I think you can take it from here. Good Luck!
