The Domain of g(x) consists of all real numbers except x = 0, since that input value would cause the function g(x) undefined. In the Similar way, the Domain of f(x) consists of all real numbers except 4. so we need to exclude the domain of g(x) that value of x for which g(x) = 4
[tex]\implies \frac{x + 1}{x} \neq 4[/tex]
[tex]\implies x + 1 \neq 4x[/tex]
[tex]\implies 3x\neq 1[/tex]
[tex]\implies x\neq \frac{1}{3}[/tex]
So, the Domain of (f o g)(x) is the set of all real numbers except [tex]\frac{1}{3}[/tex] and 0
⇒ x ≠ [tex]\frac{1}{3}[/tex] and x ≠ 0
⇒ Domain of (f o g)(x) = (-∞ , 0) ∪ (0 , [tex]\frac{1}{3}[/tex]) ∪ ([tex]\frac{1}{3}[/tex] , ∞)
