For every point on the graph of F(x), there is a point on the graph of F -1(x) with exactly the same coordinates.
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would this be false because since the second F(x) is negative wouldn't that make the numbers negative and not "exactly the same"
I think what you have would be correct for f(-x) but this is the inverse of the function f -1 where x and y are switched and would make it true.
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`For every point on the graph of F(x), there is a point on the graph of F -1(x) with exactly the same coordinates.`
this basically implies that f(x) and its inverse is the same graph. That is only true for f(x) = x and things like f(x) = 1/x. It's not true for any random f(x) function