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 x13.

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.