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1 September, 10:57

F (x) = 1/x-3, g (x) = 3X+1/x prove whether or not the functions are inverse's of each other and express the domain of the compositions using interval notation

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  1. 1 September, 11:23
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    so first lets say they are bijective so they can have inverse (you have to prove this in some exercices but here they ask you about inverse you can assume it s bijective)

    1/x-3=y

    1 = (x-3) y

    1/y=x-3

    x=1-y/y

    x=1/y-1 no because f (x) inverse=1-x/x it s not g (x)

    let s see with g (x)

    y=3x+1/x

    xy=3x+1

    3x-xy=-1

    x (3-y) = -1

    x=-1/3-y x=1/y-3 g (x) inverse=1/x-3 so f (x) is the inverse of g (x)

    the domain for g:R/{0}->R because the denumitor can t be 0 x doesn t have to be 0

    the domain of f (x) which is the same with g (x) inverse because we just prove that they are the same is f:R|{3}->R because x-3 is 0 for x=3.
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