Using the following function:$$y=\frac{mx^p+b}{d}$$... where $m$, $p$, and $b$ may be any integer
... where $d$ may be any integer $\gt0$
... and where $x$ may be any rational number $\ge0$

Is it possible to manipulate the values of the available variables to make:$$y=\sqrt[r]{x}$$... where $r$ may be any integer?
... or perhaps where $r$ may be any integer $\ge0$, or $\gt0$, if necessary?

I'm working on some computer algorithms, and it'd be very beneficial to know if roots can be represented without requiring additional operations (such as $\log$).

But if I do need to add an additional operation to the function, in order to be able to represent a wider range of possible operations (such as roots), I may be inclined to do so. I'd really prefer to avoid having to use non-integer variable values if at all possible - for performance tuning. So far I've been able to represent the bulk of basic math operations (for rational numbers) with only integer values for these variables (apart from $x$ which is somewhat special) and I'd like to keep it this way if I can.

  • 1
    $\begingroup$ Note that $\sqrt[r]0=0$ and $\frac{m0^p+b}d=\frac bd$ $\endgroup$ – Simply Beautiful Art Dec 16 '15 at 21:29

No, because $\frac{mx^{p}+b}{d}$ is rational but $y = \sqrt[r]{n}$ in general will not be (I assume you do not mean to reuse $x$ here).

  • $\begingroup$ I did intend to reuse $x$ there - that was the point. But I do see what you are saying, that makes good sense. I know it's a rudimentary question, but hearing it put in those terms makes all the difference - I think I understand it now. Thanks for the help! $\endgroup$ – Giffyguy Dec 16 '15 at 19:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.