If f(x)=x-3/x and g(x)=5x-4, What is the domain of (f•g)(x)

Answer:[tex]\{x|x\neq \frac{4}{5}\}[/tex]Step-by-step explanation:Given functions are,[tex]f(x)=\frac{x-3}{x}-----(1)[/tex][tex]g(x)=5x-4-----(2)[/tex]Now, by the property of composition of functions,[tex](fog)(x)=f(g(x))[/tex][tex]=f(5x-4)[/tex]    ( From equation (2) )[tex]=\frac{5x-4-3}{5x-4}[/tex]   ( From equation (1) )[tex]=\frac{5x-7}{5x-4}[/tex]Which is a rational function,Since, the rational function is defined for all real numbers except those real values for which denominator = 0,If 5x - 4 = 0 [tex]\implies x = \frac{4}{5}[/tex]So, the function (fog) is defined for all real numbers except 4/5,Therefore, the domain of (fog)(x) is [tex]\{x|x\neq \frac{4}{5}\}[/tex].