0
$\begingroup$

I'm having problem solving this question and I was hoping someone could help me out a bit. This is what's given:

$g(x)=x^3+x-9$

and I'm supposed to find

$\ g^{-1}\left(1\right) $

Am I supposed to just find the inverse and just plug it in? If so, could someone be kind enough to help me through a bit of the algebra? Is there any easy way of doing this?

$\ x=y^3+y-9 $

Thanks!

  • 2
    Use the *Rational roots theorem* to solve the equation $x^3+x-10=0$. As $g$ is increasing, it has only one real root. – 2017-02-13
  • 0
    @Bernard Right, thank you! – 2017-02-13

1 Answers 1

1

This may not involve algebra but still if you want to figure it out quickly then perhaps below can help ,

In $g(x)=x^3+x-9$ , we can just try by trial and error method to make the $x^3+x-9$ term equal to $1$ , so that we can get $g^{-1}(1)$ , if you see that by plugging $x = 2$ we can get $x^3+x-9 = 1$ , so that $g^{-1}(1) = 2$.

  • 0
    Ah, of course! Was missing that whole part where we could see it as $ x^3+x-9=1 $ . Thank you very much! – 2017-02-13