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Thread: [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:
    $\displaystyle
    f(x) = - f(x)$

    is 0.

    The correct definition is:

    $\displaystyle
    f(x) = f( - x)$

    b)

    $\displaystyle
    y = \sec (x) = \frac{1}
    {{\cos (x)}}$

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

    d)

    $\displaystyle
    \begin{gathered}
    y(x) = x^2 + \sin (x) \hfill \\
    y( - x) = x^2 - \sin (x) \hfill \\
    \end{gathered} $

    so obviously d is not an even function.
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