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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.

 Jan 17, 2024
 #1
avatar+307 
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Please take the time to put your answer in Latex. It helps a lot.

 

f(x)=cx4x52x+8

x32

 

Im going to try and brute force it, but its going to be really ugly.

f(f(x))=c(cx4x52x+8)4(cx4x52x+8)52(cx4x52x+8)+8

f(f(x))=c(cx4x52x+8)2(cx4x52x+8)+3

x=c2x2x+32x+32cx+6x+9

x=c2x2cx+6x+9

I think you can take it from here. Good Luck!

 Jan 18, 2024

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