]How would you solve
lim as x -> infinity f^{-1}( x^{2} + 2 x + 1)
?
Thanks!
$\displaystyle f(x) = x^2 +2x + 1 = (x+1)^2$
restricting the domain of f(x) to x > -1
$\displaystyle f^{-1}(x) = \sqrt{x} - 1$
the inverse is unbounded as $\displaystyle x \to \infty$
I'm hoping you don't have confusion between inverse and reciprocal functions.
What you wrote was $\displaystyle \lim_{x\to\infty} f^{-1}(x^2+ 2x+ 1)$ which we cannot help you with because you did not tell us what "f" is. Skeeter assumed you meant that $\displaystyle f(x)= x^2+ 2x+ 1$ and that you want to find $\displaystyle \lim_{x\to\infty} f^{-1}(x)$. Is that correct?