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Azureilai

  • one year ago

If f(x)=x^5+x^3+x, what is the inverse of f(x)? I am stuck on the fact that there are three x's on the right side and when I try to factor I can't factor anything but one y out. (I'm using x-y substitution method) Any hints would be appreciated thanks.

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  1. ganeshie8
    • one year ago
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    may i knw why do you want to find the inverse ?

  2. Azureilai
    • one year ago
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    It is extra practice I'm doing because I want to review some pre-cal stuff before calculus.

  3. ganeshie8
    • one year ago
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    i don't see any easy way to find the inverse.. could you provide more context of the problem and maybe post the actual complete question if psble

  4. geerky42
    • one year ago
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    Did you come up this question yourself?

  5. Azureilai
    • one year ago
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    Ok. The actual question gives f(x), but it asks for f\[f ^{-1}(3)\] and \[f(f ^{-1}(2))\]. No I didn't come up with it myself. It was in my book for the "before calculus" section.

  6. Azureilai
    • one year ago
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    So far I got \[x=y(y^{4}+y^{2}+1)\] and I don't know where to go from there.

  7. IrishBoy123
    • one year ago
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    solve \(x^5+x^3+x = 3\) and you'll get the inverse \(f^{−1}(3)\)

  8. ganeshie8
    • one year ago
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    actually you don't need to do any work here just notice that \(f\) eats \(f^{-1}\)

  9. ganeshie8
    • one year ago
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    \[\require{cancel}\large{f(f^{-1}(3))\\~\\ \cancel{f}(\cancel{f^{-1}}(3)) \\~\\~\\3}\]

  10. ganeshie8
    • one year ago
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    the inverse function "undoes" whatever the actual function does

  11. Azureilai
    • one year ago
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    I can see how that would apply to the second question. The answer would come out to two. But for the first question where it only ask for the inverse, should I just graph it and see what it comes out to?

  12. ganeshie8
    • one year ago
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    Ahh no, just use irishboy's hint

  13. Azureilai
    • one year ago
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    ok thank you.

  14. ganeshie8
    • one year ago
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    solve \(x^5+x^3+x = 3\) and you'll get the inverse \(f^{−1}(3)\) is it hard to guess the \(x\) value that satisfies the above equation ?

  15. Azureilai
    • one year ago
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    I see it now. wow. Thanks again.

  16. ganeshie8
    • one year ago
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    np

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