# How to find the Range of a function f(x)= (x^3+1)^-1?

Apr 13, 2015

$f \left(x\right) = {\left({x}^{3} + 1\right)}^{- 1}$
is equivalent to
$f \left(x\right) = \frac{1}{{x}^{3} + 1}$
which is valid for all Real values of $x$ except when $\left({x}^{3} + 1\right) = 0$

$\left({x}^{3} + 1\right) = 0$
implies
$x = 1$

So the Domain of $f \left(x\right)$ is all Real numbers except $1$
or in set notation
Domain of $f \left(x\right) = \left\{\left(- \infty , 1\right) \cup \left(1 , + \infty\right)\right\}$