If a(x) = 3x + 1 and g(x)=1/x-13 , what is the domain of (f*g)(x)?

For this case, the first thing you should do is multiply both functions.
 We have then:
 f (x) = 3x + 1
 g (x) = 1 / x-13
 Multiplying we have:
 (f * g) (x) = (3x + 1) * (1 / x-13)
 Rewriting the function:
 (f * g) (x) = (3x + 1) / (x-13)
 Therefore the domain of the function will be:
 x that belongs to all reals without including x = 13
  
 the domain of (f * g) (x) is:
 x that belongs to all reals without including x = 13