Question

F(x)=x+7 and , g(x)=1/x-13 what is the domain of (f*g) (x) P L E A S E H E L P A S A P !

Answer 1

The inner function g(x) has x-13 in the denominator. Set it equal to 0 and solve for x

x-13 = 0
x-13+13 = 0+13
x = 13

If x = 13 then the denominator of g(x) will be zero. This is a problem since you cannot divide by zero

So x = 13 is not allowed as an input in the g(x) function. The same applies for the composite function as well.

So that's why the domain is the set of all real numbers x but x cannot equal 13

This translates to what choice D is saying, so that is the answer