Need algebra help to Find f(g(x)) and g(f(x)), then determine if f and; g are inverses of each other

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Dec 18th, 2015

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In order to prove that f(x) is inverse of g(x), we have to show f(g(x)) = g(f(x))

Question 1:

f(x) = 6x+3 and g(x) = 6x-3

f(g(x)) = f(6x-3) = 6(6x-3)+3 = 36x-15

g(f(x)) = g(6x+3) = 6(6x+3)-3 = 36x+15

As f(g(x)) is not equal to g(f(x))

Hence f and g are not inverses of each other.

Question 2:

f(x) = 2/x and g(x) = 2/x

f(g(x)) = f(2/x) = (2)/(2/x) = 2x/2 = x

g(f(x)) = g(2/x) = (2)/(2/x) = 2x/2 = x

As f(g(x)) is equal to g(f(x))

Hence f and g are inverses of each other.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 18th, 2015

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