Find the requested function and state domain.

Find f·g, for f (x) = 1/x-5 and g (x) = 7/x

We have the following functions:

f (x) = 1 / (x-5)

g (x) = 7 / x

Multiplying the functions we have:

f · g = (1 / (x-5)) * (7 / x)

Rewriting:

f · g = (7 / x (x-5))

f · g = (7 / (x ^ 2-5x))

The domain of the function is:

All reals less:

x = 0

x = 5

Answer:

f · g = (7 / (x ^ 2-5x))

The domain of the function is:

All reals less:

x = 0

x = 5