f(x) = 9/(x - 5)

g(x) = 4/x

(fog)(x) = f(g(x)) = f(4/x) = 9/[(4/x) - 5] = 9/[(4-5x)/x] = 9x/(4-5x)

To find the domain put denominator equal to 0.

4 - 5x = 0

5x = 4

x = 4/5

So at x = 4/5 , (fog)(x) will not be defined .

Hence, domain = {x | x ≠ 4/5}

ANSWER:

(fog)(x) = 9x/(4-5x)

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