Given the functions:
[tex]\begin{gathered} f(x)=\frac{1}{x-2} \\ g(x)=\frac{4}{x} \end{gathered}[/tex]We will find the function (gof)(x)
So, we will substitute the function f(x) instead of x into the function g(x)
So,
[tex]\begin{gathered} (g\circ f)(x)=\frac{4}{\frac{1}{x-2}} \\ \\ (g\circ f)(x)=4(x-2) \\ (g\circ f)(x)=4x-8 \end{gathered}[/tex]And the function (fog)(x) will be:
[tex]\begin{gathered} (f\circ g)(x)=\frac{1}{\frac{4}{x}-2} \\ \\ (f\circ g)(x)=\frac{x}{4-2x} \end{gathered}[/tex]
