Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)
Explanation:
(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):
(6/x)/(6/x+2)
I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->
(6 +2x)/x
Do the classic keep, change, flip.
This simplifies to:
(b) Domain is all real numbers except for what makes the denominator equal to 0. 6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.