Answer:
x = 4/5 is the one x value that is not permitted. The domain of (fog)(x) is
(-infinity, 4/5) ∪ (4/5, infinity)
Step-by-step explanation:
(fog)(x) is the "composition" of f and g. We start with f(x) and replace x with g(x), which is 5x - 4:
3
f(x) = x - ------- becomes
x
3
f(5x - 4) = [5x - 4] - ------------
[5x - 4]
To identify the domain, consider the value or values of x for which the denominator shown above is zero: 5x - 4 = 0, or 5x = 4, or x = 4/5
