Answer:
- (f◦g)(x) = 8x/(3x+2)
- domain: all real numbers except x ∈ {-2/3, 0}
Explanation:
a. (f◦g)(x) = f(g(x)) = f(2/x) = 8/(2/x +3)
(f◦g)(x) = 8x/(3x+2)
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b. The domain of f(g(x)) is all real numbers except x = 0 and x = -2/3.
g(x) is not defined for x=0.
f(x) is not defined for x=-3, so f(g(x)) is not defined for g(x) = -3. g(x) = -3 for x = -2/3.
So, the domain of f(g(x)) must exclude both x=0 and x=-2/3.