Azureilai
  • Azureilai
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.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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ganeshie8
  • ganeshie8
may i knw why do you want to find the inverse ?
Azureilai
  • Azureilai
It is extra practice I'm doing because I want to review some pre-cal stuff before calculus.
ganeshie8
  • ganeshie8
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

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More answers

geerky42
  • geerky42
Did you come up this question yourself?
Azureilai
  • Azureilai
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.
Azureilai
  • Azureilai
So far I got \[x=y(y^{4}+y^{2}+1)\] and I don't know where to go from there.
IrishBoy123
  • IrishBoy123
solve \(x^5+x^3+x = 3\) and you'll get the inverse \(f^{−1}(3)\)
ganeshie8
  • ganeshie8
actually you don't need to do any work here just notice that \(f\) eats \(f^{-1}\)
ganeshie8
  • ganeshie8
\[\require{cancel}\large{f(f^{-1}(3))\\~\\ \cancel{f}(\cancel{f^{-1}}(3)) \\~\\~\\3}\]
ganeshie8
  • ganeshie8
the inverse function "undoes" whatever the actual function does
Azureilai
  • Azureilai
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?
ganeshie8
  • ganeshie8
Ahh no, just use irishboy's hint
Azureilai
  • Azureilai
ok thank you.
ganeshie8
  • ganeshie8
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 ?
Azureilai
  • Azureilai
I see it now. wow. Thanks again.
ganeshie8
  • ganeshie8
np

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