First off, I'd like to say that I'm new here and not very advanced. I'm really here in the hopes of learning something, so that my mathematical tools might match up with the mathematical level of my ideas ><.(adsbygoogle = window.adsbygoogle || []).push({});

So... First off: Is it possible for a function to contain itself? For instance, here's something I've been messing around with today:

[tex]f(x) = a ( f(x) ) +x[/tex]

Now... If I change the notation from [tex]f(x)[/tex] to [tex]y[/tex] for clarity, I get this equation, which I can rearrange in the following way:

[tex]y = ay + x[/tex]

[tex]y - ay = x[/tex]

[tex]y(1-a) = x[/tex]

[tex]y = \frac{x}{1-a}[/tex]

And, returning the notation to its original form:

[tex]f(x) = \frac{x}{1-a}[/tex]

In which case, my result (without all of the work I posted above) would be that

[tex]f(x) = a( f(x) ) + x[/tex]

is identical to

[tex]f(x) = \frac{x}{1-a}[/tex]

Is this correct, or incorrect; is there some property of functions that makes what I've done wrong? If it is correct, is there a name for this sort of "self-containing" function?

Thanks in advance for your replies... ^^

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Self-Containing Functions

**Physics Forums | Science Articles, Homework Help, Discussion**