Question

Sorry i wrote question down wrong...

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

" * " means times or multiplication

Answer 1

f(x)=x+7
g(x)=1/(x-13)
Domain (f*g)(x)=?

(f*g)(x)=f(x)*g(x)=(x+7)*[1/(x-13)]→(f*g)(x)=(x+7)/(x-13)
(f*g)(x) is a rational function, then the denominator must be different of zero:
x-13 ≠ 0
x-13 +13≠ 0+13
x ≠ 13

Then:
Domain (f*g)(x)=R-{13}=(-Infinite, 13) U (13, Infinite)
R: All the real numbers