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math

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The function f(x)=2x+8/3x-7 is one to one. Find its inverse, and check your answer.
f^-1(x)=



I haven't one clue how to do this...help me pleaaaase someone!

  • math - ,

    let y = (2x+8)/(3x-7) , notice the brackets are essential

    step1: interchange the x and y variables to form the initial inverse.

    x = (2y+8)/(3y-7)

    step: solve this new equation for y

    3xy - 7x = 2y+8
    3xy - 2y = 7x + 8
    y(3x - 2) = (7x + 8)
    y = (7x + 8)/(3x - 2)

    f^-1 (x) = (7x + 8)/(3x - 2)

    test with some value of x, say x = 3
    f(3) = 14/2 = 7
    f^-1 (7) = should get 3 back ..
    = (49+8)/(21-2) = 57/19 = 3 , looks ok

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