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Math Help - [SOLVED] f(x)=-f(x)

  1. #1
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    [SOLVED] f(x)=-f(x)

    Barron's SAT Math II. Page 12 #2
    A function is said to be even if f(x)=-f(x). Which of the following is NOT an even function

    a) y= lxl
    b)y=secx
    c) y=logx^2
    d) y=x^2+sinx
    e) y=3x^4-2x^2+17

    I know a), c) and e) are even functions. But I can't decide between b) and d). What does sec in y=secx mean exactly?

    Thanks in advance! (:
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  2. #2
    Senior Member Peritus's Avatar
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    first of all the definition of even function as you present it is wrong, the only function that satisfies:
    <br />
f(x) =  - f(x)

    is 0.

    The correct definition is:

    <br />
f(x) = f( - x)

    b)

    <br />
y = \sec (x) = \frac{1}<br />
{{\cos (x)}}

    and we already know that cos(x) is an even function, thus b is even.

    d)

    <br />
\begin{gathered}<br />
  y(x) = x^2  + \sin (x) \hfill \\<br />
  y( - x) = x^2  - \sin (x) \hfill \\ <br />
\end{gathered}

    so obviously d is not an even function.
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