y = 1/x is symmetric with respect to the y = x.
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Find the inverse function.
Namely,
y = 1/x
==> x = 1/y
so, y = 1/x is inverse function.
so, same graph.
so, this is symmetric with respect to the y = x.
I suppose so: this is x*y = 1 , and multiplication is commutative.
Could your method show symmetry for x^2 + y^2 = 1 ?
Or x*y = 0 ?