Answer
The solutions are
$f^{-1}(3)=1.$
$f(f^{-1}(2))=2.$
Work Step by Step
By noticing that
$f(1)=1^5+1^3+1=3$
we get by the definition of the inverse function that
$f^{-1}(3)=1.$
For the second part we will use the following property:
If $f(x)=y$ then $f^{-1}(y)=x$ so $f(f^{-1}(y))=f(x)=y$. Applying this to our problem:
$$f(f^{-1}(2))=2.$$
