Phenom wrote:is x<x^2 ?' to 'is 0<x?' i.e, 'Is 'x' positive?' ??
Is x<x²?
0 < x²-x.
0 < x(x-1).
The critical points are x=0 and x=1.
These are the only values of x where x(x-1) = 0.
When x is any other value, x(x-1)<>0.
To determine the range of x, try one value to the left and right of each critical point.
x<0:
Plugging x=-1 into x<x², we get:
-1<(-1)²
-1<1.
This works.
x<0 is part of the range.
0<x<1:
Plugging x=1/2 into x<x², we get:
1/2<(1/2)²
1/2<1/4.
Doesn't work.
0<x<1 is NOT part of the range.
x>1:
Plugging x=2 into x<x², we get:
2<(2)²
2<4
This works.
x>1 is part of the range.
Since the only values not included in the range of x are 0≤x≤1, the question rephrased:
Is 0≤x≤1?
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