# Math Help - finding examples for functions

1. ## 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.

2. 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.

3. thanks for the second example! but in the first one I need a function that not defined in a split domain!!!
l

4. Originally Posted by omert
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 $\ln\left(\frac{1}{x^{2n}}\right)~n\in\mathbb{N}$