Math(Please check)

The following function is one-to-one; find its inverse

f(x)=x^3+5

I know that the first step would be to set y = to x so I did y=x^3+5

Then you swap x with y so x=y^3+5.

Then you solve for y and this is where I think i messed up. I did
y^3=x-5 = y=x^3-5

Then the inverse would be f^-1(x)=x^3-5

Is this correct or did I do that last step wrong?

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asked by Hannah
  1. Your error is in solving for y in
    x = y^3 + 5

    y^3 = x-5 , you had that
    y = cuberoot(x-5) or (x-5)^(1/3)

    check:
    let x = 2 in the original y = x^3+5
    y = 2^3+5 = 13

    now let x = 13 in the invers
    y = cuberoot(13-5
    = cuberoot(8)
    = 2

    which is what we started with

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    posted by Reiny
  2. So what is the inverse?

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    posted by Hannah
  3. I stated it ....

    y = cuberoot(x-5)
    or
    y = (x-5)^(1/3)
    or
    f(x) = (x-5)^(1/3)

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    posted by Reiny
  4. O ok I understand. Thanks!!

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    posted by Hannah

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