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Öskå
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y1[x_] := Sqrt@x - 1
y2[x_] := -Sqrt@ x + 1
Plot[{y1[x], y2[x]}, {x, 0, x /. Last@Solve[y1[x] == y2[x]]}, PlotRange->{{0, 2}, {-1, 1}}]

Mathematica graphics

or you can play with PlotRange:

Plot[{y1[x], y2[x]}, {x, 0, 10}, 
  PlotRange -> {{0, x /. Last@Solve[y1[x] == y2[x]]}, {-1, 1}}]

Mathematica graphics

y1[x_] := Sqrt@x - 1
y2[x_] := -Sqrt@ x + 1
Plot[{y1[x], y2[x]}, {x, 0, x /. Last@Solve[y1[x] == y2[x]]}, PlotRange->{{0, 2}, {-1, 1}}]

Mathematica graphics

y1[x_] := Sqrt@x - 1
y2[x_] := -Sqrt@ x + 1
Plot[{y1[x], y2[x]}, {x, 0, x /. Last@Solve[y1[x] == y2[x]]}, PlotRange->{{0, 2}, {-1, 1}}]

Mathematica graphics

or you can play with PlotRange:

Plot[{y1[x], y2[x]}, {x, 0, 10}, 
  PlotRange -> {{0, x /. Last@Solve[y1[x] == y2[x]]}, {-1, 1}}]

Mathematica graphics

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Dr. belisarius
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y1[x_] := Sqrt@x - 1
y2[x_] := -Sqrt@ x + 1
Plot[{y1[x], y2[x]}, {x, 0, x /. Last@Solve[y1[x] == y2[x]]}, PlotRange->{{0, 2}, {-1, 1}}]

Mathematica graphics

Post Made Community Wiki by Dr. belisarius