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Math Help - finding examples for functions

  1. #1
    Junior Member
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    finding examples for functions

    I wanted to find an example for a function that maintains the following conditions:
    1. f(x)=? if all the following conditions are correct.
    2. if all the following conditions are correct: f(x) is a function that defined in a split domain. I need to find examples for f(x);x>=0 and for f(x);x<0.
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  2. #2
    Junior Member Ziaris's Avatar
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    For the first one, one example is f(x) = \delta(x) with \delta(x) being the delta function defined as

    \delta(x) = \begin{cases} \infty, & x = 0 \\ 0, & x \ne 0 \end{cases}.

    I'm not quite understanding what you're asking for in your second problem. A piecewise function that satisfies the limits provided is

    f(x) = \begin{cases}\frac{1}{x+1/2}, & x\geq 0 \\ x+6, & x<0 \end{cases}.

    Hopefully that's what you meant.
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  3. #3
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    thanks for the second example! but in the first one I need a function that not defined in a split domain!!!
    l
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by omert View Post
    thanks for the second example! but in the first one I need a function that not defined in a split domain!!!
    l
    f(x)=\frac{1}{\sqrt{|x|}}. You can find a million examples, all they need to do is fill three criterion: they are dominated by x as x goes to zero, they are even, and obviously the second criterion you set. Some other examples would be f(x)=\ln\left(\frac{1}{|x|}\right) or \ln\left(\frac{1}{x^{2n}}\right)~n\in\mathbb{N}
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