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.
Please take the time to put your answer in Latex. It helps a lot.
f(x)=cx4x−5−2x+8
x≠−32
Im going to try and brute force it, but its going to be really ugly.
f(f(x))=c(cx4x−5−2x+8)4(cx4x−5−2x+8)−5−2(cx4x−5−2x+8)+8
f(f(x))=c(cx4x−5−2x+8)2(cx4x−5−2x+8)+3
x=c2x2x+3⋅2x+32cx+6x+9
x=c2x2cx+6x+9
I think you can take it from here. Good Luck!