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Algebra

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Which would be the inverse of this:

Let f(x)=(x+3)(2x-5)


f^ (-1) x = (5x - 3)/ (2x + 1)

f^ (-1) x = (5x + 3)/ (2x - 1)

  • Algebra -

    Could you check if there wasn't a typo, namely,
    "Let f(x)=(x+3)/(2x-5)... "
    If that's the case, it's the second response.
    To double check,
    let g(x)=f-1(x)=(5x+3)/(2x-1)
    Evaluate
    f(g(x))
    = ((5x+3)/(2x-1)+3)/((2(5x+3))/(2x-1)-5)
    = x

  • Algebra -

    Let y = f(x)

    y = (x + 3)/ (2x - 5)

    Switch x and y.

    x = (y + 3)/ (2y - 5)

    Multiply both sides by (2y - 5).

    2xy - 5x = y + 3

    Subtract 3 from both sides.

    2xy - 5x - 3 = y

    Subtract 2xy from both sides.

    -5x - 3 = -2xy + y


    Factor the right side.

    -5x - 3 = y (-2x + 1)

    Divide both sides by (-2x + 1).

    (-5x - 3)/ (-2x + 1) = y

    (5x - 3)/ (2x + 1) = y

    Now we replace y with the inverse function notation: f^ (-1) x.

    f^ (-1) x = (5x + 3) / (2x - 1)

    This my work to reflect the answer. Is it correct? Thanks!

  • Algebra -

    Yes, the calculation is correct.

    Note: You may not have noticed that you omitted the division sign in the initial post.

  • Algebra -

    Thanks for pointing that out!

  • Algebra -

    You're welcome!

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