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Determine which functions are ODD (symmetry with origin): a. f(x) = 2x^3 + x + 3 b....
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A real valued function is said to be odd when the following condition satisfies.
`-f(x) = f(-x)`
Let us consider our functions.
`a. f(x) = 2x^3 + x + 3`
`f(-x) = -2x^3-x+3 != -f(x) `
`b. f(x) = 2x^3 + x`
`f(-x) = -2x^3-x = -(2x^3+x) = -f(x)`
`c. f(x) = 2x^3 + x^2 + x + 3`
`f(-x) = -2x^3+x^2-x+3 != -f(x)`
`d. f(x) = 4x`
`f(-x) = -4x = -f(x)`
`e. f(x) = x^3 +|x|`
`f(-x) = -x^3+|-x| = -x^3+|x| != -f(x)`
`f. f(x) = 2x + 1/x`
`f(-x) = -2x-1/x = -(2x+1/x) = -f(x)`
So the odd functions are the functions at b,d and f.
If you have a constant term in your function that will never be a odd function (as a and c)
If you have a even degree polynomial you will never get a odd function.
Posted by jeew-m on June 15, 2013 at 5:29 AM (Answer #1)
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