What's the #f^(-1)(x)# of #f(x)=x^3+1/x+2 ?#

1 Answer
Jan 10, 2018

It is not going to be easy.... It involves #x# to the #3#rd and #4#th powers, which are extremely ugly to solve.

Explanation:

We say that #f^-1(x)# is the inverse function of #f(x)#. That means, if #f(x)=y=...x+...#, we express #x# in terms of #y#.

#f(x)=x^3+1/x+2#

#y=x^3+1/x+2#

#x^4+2x+1=xy#

From here, I couldn't solve it, so I used Wolfram-Alpha, and got the following result:

http://www4d.wolframalpha.com/Calculate/MSP/MSP17521a097e687h3i88f00003705i975e921gb8a?MSPStoreType=image/gif&s=39&w=541.&h=544.