For this case we have the following functions:
[tex]f (x) = \frac {x - 3} {x}\\g (x) = 5x - 4[/tex]
The first thing we should do is the composition of functions.
We have then:
[tex]f (g (x)) = \frac {(5x - 4) - 3} {5x - 4}[/tex]
Rewriting we have:
[tex]f (g (x)) = \frac {5x - 7} {5x - 4}[/tex]
Therefore the domain of the function are the values of x that define the function.
The function is not defined for:
[tex]5x - 4 = 0\\5x = 4\\x = \frac {4} {5}[/tex]
Answer:
The domain of the function is:
All real numbers except [tex]\frac {4} {5}[/tex]
