anonymous
  • anonymous
Evaluate the inverse of the function y=x^3+x.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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raffle_snaffle
  • raffle_snaffle
solve for x
raffle_snaffle
  • raffle_snaffle
once you obtain x, replace x with y then you get your inverse function.
anonymous
  • anonymous
Is it easy to write x in terms of y? surely not...

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anonymous
  • anonymous
\[y=x^3+x\]\[x=y^3+y\]\[0=y^3+y-x\] oh, that looks unappealing... :l
anonymous
  • anonymous
Cardan's method can be used here, but yields very unappealing answers...
raffle_snaffle
  • raffle_snaffle
can you use a calculator?
anonymous
  • anonymous
Let \(y=c\):\[ 0 = x^3+x-c \]Plug this into the equation for cubic functions to find generic answers in terms of \(c\). \(f(c) = y^{-1}(x)\)
anonymous
  • anonymous
the cubic formula will give you 3 answers so you'll probably have to use test points to figure out which ones apply where. It works, though it isn't elegant.

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