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Answer:
(a) f(g(x)) = g(f(x)) = x; functions are inverses
(b) f(g(x)) = g(f(x)) = x +4; functions are not inverses
Explanation:
(a)
f(g(x)) = f(1/(6x)) = 1/(6(1/(6x))) = 1/(6/(6x)) = 1/(1/x)
f(g(x)) = x
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g(f(x)) is the same, because f(x) = g(x).
g(f(x)) = x
- f and g are inverses of each other
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(b)
f(g(x)) = f(x +2) = (x +2) +2
f(g(x)) = x +4
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g(f(x)) is the same, because f(x) = g(x).
g(f(x)) = x+4
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- f and g are not inverses of each other