I am working on a paper to find the equation of the inverse function of a cubic function. The function is(adsbygoogle = window.adsbygoogle || []).push({});

f(x) = x^3 + 6x^2 +12x +7

I have already graphed the function and its inverse. I have found the inflection point of (-2, -1). I found the 3 roots (1 real & 2 complex). The real root is x=-1, so I am left with:

(x+1)(x^2 + 5x + 7)

which leads to the complex roots of:

.(5+i(3)^.5)/2 and (5 - i(3)^.5)/2

At this point though I am totally stuck. I know that I am supposed to switch the placement of the x & y variables, but I can't figure out what the next step should be. So I now have:

x = y^3 + 6y^2 +12y +7,

but I have no idea what to do with it! I know from above that it can be rewritten as:

x = (y+1)(y^2 + 5y + 7).

How do I get the y variable all by itself though? Looking for some direction on what I should do at this point to come up with the equation of the inverse.

Thanks for your help in advance!

Nan

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# Inverse of a Cubic Function

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