Question

Determine the domain of the function (f*g)(x) where f(x) =3x-1/x-4 and g(x) =x+1/x

Answer 1

(-00,4)U(4,00)

Or C

Answer 2

Domain = R- {0,4}

Explanation:

`f(x) =(3x-1)/(x-4)`

`g(x) =(x+1)/(x)`

`(f*g)(x)=(3x-1)/(x-4) * (x+1)/(x)`

`(f*g)(x)=((3x-1)(x+1))/((x-4)(x))`

In order to function (f*g)x to be defined , the Denominator must not be equal to zero.

Hence

x ≠ 0

(x-4) ≠ 0 ⇒ x≠4

Hence (f*g)x is defined for all values of x except 0 and 4

Hence Domain = R- {0,4}