title: If R(x) is a random function, is R(x) || R(x') also a random function?
body: <p>If R(x) is a random function,  is R(x) || R(x') also a random function ? </p>
  
  <p>R(x) is random in the true sense.</p>
  
  <p>x is a bit string over 0s and 1s.</p>
  
  <p>x' is complement of x.</p>
  
  <p>|| is the simple concatenation</p>
  
  <p>Edit : </p>
  
  <p>This R(x) is selected randomly from the family of functions {0,1}^k -> {0,1)^k. Once R(x) has been chosen, it gets fixed. Thus Same input will generate same output. Length of R(x) is fixed (k, say 32) </p>
  
  <p>G(x) = R(x) || R(x')</p>