Consider a function f(x) such that f(5x) =x-5/5x-1. Find f(x) and hence write down the domain of f(x).

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Step-by-step explanation:

To find f(x), you can replace x in the given function with (x/5).

  f(5(x/5)) = (x/5 -5)/(5(x/5) -1)

  f(x) = (x/5 -5)/(x -1)

  f(x) = (x -25)/(5(x -1))

  f(x) = (x -25)/(5x -5)

The only domain restriction is that x cannot make the denominator zero:

  x cannot be 1. (The domain is all real numbers except 1.)