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xΙxΙ is odd function or even function?
Asked by Rahul Srivastava Last Modified
Answer 
See, if you expand the function x|x|, you will get (square of x) in (0,∞). But (negative of the square of x)-
in (-∞ ,0). so now if you plot the graph, the graph will be downward parabola in one part of the x-axis and another upward parabola. So, it is neither odd nor even.
The graph of an even function is symmetric w.r.t. Y-axis. Is is an even function.
The graph of an odd function has rotational symmetry w. r. t. the origin. X is an odd function.
= xΙxΙ =
in (0,
) and -
in (-
, 0).
Therefore, f(-x) = in (0,
) and -
in (-
, 0).
| x | 1 | 2 | 3 | 4 |
| 1 | 4 | 9 | 16 | |
| - | -1 | -4 | -9 | -16 |
The half part of graph comes in first quadrant and the other half comes in the fourth quadrant . So, it is neither odd nor even.
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