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