Question 1024199
1.  {{{x^3 = 8}}} ==> x = 2

2.  {{{f^(-1)(6) = -8}}} ==> f(-8) = 6.

3.  f(2) = 5 ==> {{{f^(-1)(5)=2}}}.  (f(5)=−4 is only a distraction.)

4.  {{{f(x) = y = 2x^3+1}}} ==> {{{(y-1)/2 = x^3}}} ==> {{{root(3,(y-1)/2) = x}}} ==> {{{f^(-1)(x) = root(3,(x-1)/2)}}}.  The original function would have an inverse because {{{f(x)= 2x^3+1}}} is a one-to-one function.

5.  I leave this up to you.