To find if the pairs are inverse of each other, find their composition. The composition of the inverse function will always be equal to x.
For first option, the composition will be:
[tex]f(g(x))=2+ \sqrt[3]{2- x^{3} } [/tex]
For second option, the composition will be:
[tex]f(g(x))= \frac{6x-8}{6}+8= \frac{6x-8+48}{6} = \frac{6x-40}{6} [/tex]
For third option, the composition will be:
[tex]f(g(x))= \frac{49}{x+9}-9 [/tex]
For Fourth option, the composition will be:
[tex]f(g(x))=5( \frac{x+11}{5})-11=x+11-11=x [/tex]
So the pair of function given in Fourth option are inverse of each other
