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In the case of the function $f(x)=x^2+x^4$ is there any trick to inversing it? as the only ways I know do not work on it. As you cannot make y the subject through rearranging it.

Thanks in advance.

Gregory
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Mathlete
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  • It's quadratic in $u=x^2$. – Matthew Leingang Oct 28 '17 at 15:48
  • Can you solve a quadratic equation? Since you have an even function here, you will get multiple possible values for the inverse. Do you have a protocol for choosing which you want? – Mark Bennet Oct 28 '17 at 15:49
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    In general, no there is no trick to finding the inverse. One idea is to exchange $y$ and $x$. In your example you would $$ x = y^2 + y^4 $$ and solve for $y$, this would be your inverse. – Gregory Oct 28 '17 at 15:50
  • ah thank you, I did not even think of that. – Mathlete Oct 28 '17 at 15:52
  • This function doesn't have a unique inverse (assuming that the domain is the set of all real numbers). – paw88789 Oct 28 '17 at 15:58

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Setting $$y=x^2+x^4$$ we get $$x^4+x^2-y=0$$ solving this using the quadratic formula we obtain $$x^2_{1,2}=-\frac{1}{2}\pm\sqrt{\frac{1}{4}+y}$$ can you go on?

Dr. Sonnhard Graubner
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  • the thing is, I never done inverse with quadratics before, so the whole thing in general is new ,but thanks – Mathlete Oct 28 '17 at 18:35