Determining whether a Function is Even or Odd
Date: 11/09/1999 at 00:06:41 From: Nick Lanning Subject: Odd and Even Functions How do you determine whether each function is an even function, an odd function, both or neither? The problems are as follows: y = x^5 - 4x y = 6x^3 - 3x + 5 y = x^2 - 64 I am stuck on how to get started and what steps I should take. Can you help me?
Date: 11/09/1999 at 10:54:08 From: Doctor Rob Subject: Re: Odd and Even Functions Thanks for writing to Ask Dr. Math, Nick. Test for evenness: Substitute for (x,y) the pair (-x,y), and solve the two equations simultaneously. If the equations are dependent, the function is even. Test for oddness: Substitute for (x,y) the pair (-x,-y), and solve the two equations simultaneously. If the equations are dependent, the function is odd. Example: Test whether y = x^5 - x is even. y = (-x)^5 - (-x), y = x^5 - x, and, subtracting the first from the second, 0 = 2*(x^5 - x), which is false if x = 2, for example. Thus the function is not even. Example: Test whether y = x^5 - x is odd. -y = (-x)^5 + (-x), y = x^5 - x, and, adding these, 0 = 0, which is true for all values of x, which means the two equations are dependent, and the function is odd. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/
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