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].
