Continuous function/Intermediate value theorem/Value c/Exercise

We consider the mapping ${}f\colon \mathbb {R} \setminus {\{0,1\}}\rightarrow \mathbb {R}$ given by

${}f(x)={\frac {1}{x^{3}}}+{\frac {1}{(x-1)^{3}}}\,.$

Show, using the intermediate value theorem, that ${}f$ obtains every value ${}c\neq 0$ at least in two points.

Create a solution