For the function f(x)==2x, I get why the inverse function is f^-1(y)==y/2, but why is it ok to write it equivalently as f^-1(x)==x/2? x and y are specific objects, in this case y ==2x and x==y/2. So x and y are not equal. I do not get why you can just interchange them?

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http://en.wikipedia.org/wiki/Free_variables_and_bound_variables

When a variable is used as a function input, it becomes a place holder for the sake of substitution.

Saying that \(
f(x) = x^2
\) and \(
f(y) = y^2
\) isn't saying that \(
x = y
\).

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