Function Composition
Given the function f(x)=1x2\displaystyle {f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}-{2}}}} and the function g(x)=4x+2\displaystyle {g{{\left({x}\right)}}}={\frac{{{4}}}{{{x}}}}+{2} determine each of the following. Simplify your answers.
Evaluate f(g(x))\displaystyle {f{{\left({g{{\left({x}\right)}}}\right)}}}f(g(x))=\displaystyle {f{{\left({g{{\left({x}\right)}}}\right)}}}=
 
Evaluate g(f(x))\displaystyle {g{{\left({f{{\left({x}\right)}}}\right)}}}g(f(x))=\displaystyle {g{{\left({f{{\left({x}\right)}}}\right)}}}=