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

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Answer 1 · 2015-04-13T13:28:45

$f(x) = (x^3+1)^(-1)$
is equivalent to
$f(x) = 1/(x^3+1)$
which is valid for all Real values of $x$ except when $(x^3+1) = 0$

$(x^3+1) = 0$
implies
$x=1$

So the Domain of $f(x)$ is all Real numbers except $1$
or in set notation
Domain of $f(x) = {(-oo,1) uu (1,+oo)}$

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