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How do you find out if the function is a even odd or neither I know your supposed to use f-x -fx but I am not so sure how to do it the problem is 2x to the third power minus x squared?
Wiki User
∙ 10y ago
An even function is symmetric around the vertical axis. An odd function - such as the sine function - has a sort of symmetry too - around the point of origin. If you graph this specific function (for example, on the Wolfram Alpha website), you can see that the function has none of these symmetries. To prove that the function is NOT even, nor odd, just find a number for which f(x) is neither f(-x) nor -f(-x).
Actually proving that a function IS even or odd (assuming it actually is) is more complicated, of course - you have to prove that it has the "even" or the "odd" property for EVERY value of x.
Let f(x) = 2x3 - x2. Notice that f is defined for any x, since it is a polynomial function.
If f(-x) = f(x), then f is even.
If f(-x) = -f(x), then f is odd.
f(-x) = 2(-x)3 - (-x)2 = -2x3 - x2
Since f(-x) ≠ f(x) = 2x3 - x2, f is not even.
Since f(-x) ≠ - f(x) = -(2x3 - x2) = -2x3 + x2, f is not odd.
Therefore f is neither even nor odd.
Wiki User
∙ 10y ago
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Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
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