Yes, because the hint was to prove $\displaystyle f(x) > g(x)$ and we wanted to prove $\displaystyle x^n > x$ so it makes sense to assume $\displaystyle g(x)=x$.
how about I do this
Factorise! $\displaystyle x^n-x=x(x^{n-1}-1)=x(x-1)(1+x+x^2+\cdots+x^{n-2}),$ the product of three terms which are obviously positive for $\displaystyle x\,>\,1.$
does this make sense?
Last edited by Jameson; Nov 24th 2009 at 02:20 PM.