If fx)=x+7 and g(x)= 1/x-13, what is the domain of (f*g)(x)

F * g means exactly that.

Which is that you should multiply the definitions of the functions.
(x+7)(1/x-13)  = x/x-13 + 7/x-13 = x+7/x-13

x+7/x-13

The domain of this function, is x<13 and x>13.
But not 13. Because 13-13 = 0
And it is not legal to divide a number by 0.
Hence, f*g(13) is not defined.