Algebra

How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

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asked by Kenya
  1. Let's try this for f(x)= y = e^(6x)

    Step 1:
    interchange x and y to get
    x=e^(6y)

    Step 2:
    solve for y in terms of x:
    ln(x) = ln(e^(6y)) = 6y
    y = ln(x)/6
    So
    f-1(x) = ln(x)/6

    Step 3:
    Verify that f(f-1(x))=x (if the inverse was correct).
    f(f-1(x))
    =f(ln(x)/6)
    =e^(6*ln(x)/6)
    =e^(ln(x))
    =x
    So the inverse is correct.

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    posted by MathMate
  2. Ok that's slightly confusing.
    I understand the flipping of x and y but then what do you do?
    so x=log8 y
    ?

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    posted by Kenya
  3. Yes, then you solve for y in terms of x.
    use the law of exponents:
    elog(x)=x
    or
    8log8 y=y, etc.
    (assuming log8 y is log(y) to the base 8)
    raise both sides to power of 8 to get
    8x = 8log8(y)<?sup>
    Simplify and solve y in terms of x.

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    posted by MathMate
  4. 8x = 8log8(y) = y
    Simplify and solve y in terms of x.

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    posted by MathMate
  5. MMMMmmmmmmk that helps, thanks!

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    posted by Webber
  6. You're welcome!

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    posted by MathMate

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