- #1

etotheipi

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I saw something in my notes that I didn't understand... we have ##y=f(x)##, and consider an implicit equation of the form ##g(y) = f(x)##. They then say that ##f=g##. Why is that true? I would have thought$$f = \{ (a,f(a)) : a\in \mathbb{R} \} \subseteq \mathbb{R}^2$$whilst ##g## is just$$g = \{ (a,a) : a\in \mathbb{R} \} \subseteq \mathbb{R}^2$$What am I missing? Thanks!