You can
put this solution on YOUR website! Determine whether g(x)=3x-6 and f(x)=1/3x+2 are inverse functions.
Thank you
f(x) and g(x) are inverses if and only if their composition equals the
identity function I(x) = x. That is, if
fog(x) = f(g(x)) = gof(x) = g(f(x)) = x
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fog(x) = f(g(x)) = f(3x-6) = 1/3(3x-6) + 2 = x - 2 + 2 = x
That's half of it.
gof(x) = g(f(x)) = g(1/3x+2)) = 3(1/3x+2) - 6 = x + 6 - 6 = x
Therefore f(x) and g(x) are inverses.
Edwin
