Question

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

Answer 1

`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)}`