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Mathematics
Loosetooth
1 July, 13:39
0≤x²≤2 how does one do this?
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Chasity Pratt
1 July, 15:46
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First, you may want to visualize what is happening here.
Graph y=x^2. The graph is that of a parabola that opens up. Draw a horizontal line through y=2 and another through y=0 (which is really the x-axis). Put dots where the curve intersects these lines.
Draw vertical lines through the two dots where the curve intersects the horiz. line y=2. Note where these two lines intersect the x-axis. From your graph, you can approximate the domain: it is roughly [-1.414, 1.414], or [-sqrt (2), - sqrt (2).
You could also take the sqrt of all 3 terms in the given inequality.
Then sqrt (0) ≤ sqrt (x²) ≤ sqrt (2), which is equivalent to 0 ≤ |x| ≤sqrt (2).
This allows for negative x in [-sqrt (2),).
The domain of this function is [-sqrt (2), + sqrt (2) ].
The range is 0 ≤ y ≤ 2.
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