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Math Help - Help: Definition of function

  1. #1
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    Help: Definition of function

    Greetings.

    For a function, f(x), defined as follows:

    1 if |x| < (1/2)
    0 otherwise

    how will the function f(-x) be defined?

    Would greatly appreciate assistance.

    Best regards,
    wirefree
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  2. #2
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    For a function, f(x), defined as follows:

    1 if |x| < (1/2)
    0 otherwise

    how will the function f(-x) be defined?

    1 if -.5 < -x < .5
    0 otherwise

    Seems like the only plausible answer to me.
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  3. #3
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    Quote Originally Posted by Isimbot View Post
    1 if -.5 < -x < .5
    0 otherwise

    Seems like the only plausible answer to me.
    Appreciate the prompt response, Isimbot.

    Your response implies:

    f(x) = f(-x)

    Is this true for all functions?

    Look forward to your response.

    Best regards,
    wirefree
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  4. #4
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    Quote Originally Posted by wirefree View Post
    Greetings.

    For a function, f(x), defined as follows:

    1 if |x| < (1/2)
    0 otherwise

    how will the function f(-x) be defined?
    since |x| = |-x| , the function will be the same.
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  5. #5
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    Quote Originally Posted by wirefree View Post
    Appreciate the prompt response, Isimbot.

    Your response implies:

    f(x) = f(-x)

    Is this true for all functions?

    Look forward to your response.

    Best regards,
    wirefree
    With the stated definition, yes.
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  6. #6
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    Quote Originally Posted by wirefree View Post
    Appreciate the prompt response, Isimbot.

    Your response implies:

    f(x) = f(-x)

    Is this true for all functions?

    Look forward to your response.

    Best regards,
    wirefree
    No, of course not. It is true for all "even" functions- in fact, that is precisely the definition of "even function". And the function you gave is an even function.
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  7. #7
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    |x|, by definition, is even.

    Appreciate the help.

    Best regards,
    wirefree
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