Basic functional equation

function

find at least on real function which is defined by  : f( k * x) = f (x) for all x Real and k real

  • Obviously all constants satisfies the equation above , but you can say more if f is continue at x=0 , then f is a constant function
  • a non trivial example of a solution of equation above could be : x → sin( 2π * ln(x) )           with k = e, you can notice that this function is not continue at x = 0
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