Question

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Answer 1

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.
`(6)/(x) * (x)/(6+2x)`

This simplifies to:
`(6)/(6+2x)`

(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.