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Given f(x)=2-3x and g(x)=hx+k where h and k are constants.If gf(-1)=6 and g^-1(4)=g(4),find the possible values of h and k?

  • math -

    First write expressions for gf(x) and g^-1(x) in terms of h and k.

    Then write equations for gf(-1) and g^(-1)(4)

    This will leave you with two equations that involve only h and k.

    Solve them simultaneously.

    For starters,
    gf(x) = h(2-3x) + k = 2h -3hx + k
    gf(-1) = 2h + 3h + k = 5h + k

    Now compute the inverse function of g and complete the solution.

    See if you get
    g^-1(x) = [(x-k)/h] + k

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