How to plot $x^2$ over $-5<x<-1\cup1<x<5$

You can also define f conditionally:

f[x_] := x^2 /; (-5 < x < -1 || 1 < x < 5)

With

reg = ImplicitRegion[-5 < x < -1 || 1 < x < 5, x]

reg = Interval[{-5, -1}, {1, 5}]

Plot[x^2, {x} ∈ reg]

enter image description here

EDIT

This might work for v7:

Plot[If[-5 < x < -1 || 1 < x < 5, x^2], {x, -5, 5}]

In V8 and up, one can use ConditionalExpression:

Plot[ConditionalExpression[x^2, -5 < x < -1 || 1 < x < 5], {x, -5, 5}]

Mathematica graphics

Response to updated question

This might work in all versions of Mathematica:

Show[
 Plot[x^2, {x, -5, -1}],
 Plot[x^2, {x, 1, 5}],
 PlotRange -> All]

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