Self-Inverse Function?

Algebra Level pending

Let a,b,ca, b, c be integers such that the function  f(x)=axbcx  \ f(x) = \large \frac{ ax-b} { cx} \ has the following properties:

  • f(1)=2.5 f(1) = -2.5
  • f(5)=0.5 f(5) = -0.5
  • f(f(x))=x f(f(x) ) = x

Find f(20)f(-20).

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