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



===========================================================



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

   

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