Question

Need some help with this paper

Answer 1

well, it comes down to, if f(x) is indeed an inverse of g(x) and the other way around, then f( g(x) ) = x, and likewise g( f(x) ) = x, so let's check if f( g(x) =x

`f(x)=3x+11\hspace{5em}g(x)=-\cfrac{1}{3}x-\cfrac{11}{3} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=3\left( -\cfrac{1}{3}x-\cfrac{11}{3} \right)+11 \\\\\\ f(~~g(x)~~)=-x-11+11\implies f(~~g(x)~~)=-x ~~ \bigotimes`

now, we could do a test by doing g( f(x) ), however we don't need to, since f( g(x) ) ≠ x, they're not inverse of each other.