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

Answer:

Domain = R- {0,4}

Step-by-step explanation:

$f(x) =\frac{3x-1}{x-4}$

$g(x) =\frac{x+1}{x}$

$(f*g)(x)=\frac{3x-1}{x-4} \times \frac{x+1}{x}$

$(f*g)(x)=\frac{(3x-1)(x+1)}{(x-4)(x)}$

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}