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First of all, consider the cubic equation $$x^3 + a = x. $$

Using Mathematica is easy to find real solutions of the above equation,

F[a_]:= Solve[x^3 + a == x , x, Reals]

Now, I would like to plot the graph of the multivalued function $$G: [-1,1]\to 2^\mathbb{R}$$ $$a \mapsto\ \{\text{the real solutions of }x^3 + a =x\}, $$ i.e. the set

$$\text{Graf}(G):= \{(x,y);\ x\in [-1,1]\ \text{and}\ y\in G(x)\}. $$

Can anyone help me?

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Is this what you're looking for?

ContourPlot[x^3 + a == x, {a, -1, 1}, {x, -2, 2}, FrameLabel -> {a, x}]

enter image description here

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  • $\begingroup$ You are right, I forgot about ContourPlot. Thx!!! $\endgroup$ – Matheus Manzatto Jul 27 at 21:53

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