Determime the domain of the function (f * g)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x
+129840 Determime the domain of the function (f * g)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x
(f * g) (x) =
[ 3x -1 ] / [ x - 4 ] * [ x + 1/x ]
[3x^2 - x + 3 - 1/x] / [ x - 4] =
[3x^3 - x^2 + 3x - 1] / [ x (x - 4]
Note that the numerator will be defined for all x........the denominator will be 0 whenever x = 0 or x = 4
So....the domain is ( -inf, 0 ) U (0, 4) U (4 , inf )
Here's a graph : https://www.desmos.com/calculator/hla8abgse6
