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Question

The number of point of intersection of the curve y=max{x23x+2,2} with the xaxis is

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Solution

Given, y=max{x23x+2,2}
Let f(x)=x23x+2 and g(x)=2
x23x+2=2
x=0,3 (Points of intersection)
To draw the given curve, we have to draw the graph of f(x)=x23x+2 (parabola) and g(x)=2 (horizontal line), Neglecting the graph below the points of intersection.

So, the curve do not intersect the xaxis

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