Problem 52973. Easy Sequences 45: Second Derivative of Inverse Polynomial Function

Created by Ramon Villamangca

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The inverse of a function, is the function , that reverses f. That means that if , then . For example, the function to convert celsius temperature to fahrenheit is: , the inverse function (convert from fahrenheit to celsius) is: . So that,  and .
Given a polynomial function P (presented as vector of numbers), and a value n, if , write a program that evaluates , where . 
For example, if , and , then  and . Therefore .
NOTE: It is possible for  to return some complex numbers. We are interested only with real values, so in cases where there are no real , please output an empty vector. Also please round-off your output to 4 decimal places, and sorted in ascending order.

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William on 31 Oct 2021

I haven't quite figured out what problem 8 is supposed to do. I am getting a large number of real solutions, mostly 0.0 or 0.0001. I used unique() to reduce the solution to four values. These values are all correct except that they include 0.0.

Ramon Villamangca on 1 Nov 2021

Hi William, I missed to write "0.0000" in the solution set of test #8. Sorry for that. Corrected it.

Please rate the problem. Thanks.

Tim on 2 Nov 2021

For problem 8 I see only three real solutions--none that give R=0.0000.

Tim on 4 Nov 2021

I see now--you want to round off R before testing for an imaginary part.

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Problem 52973. Easy Sequences 45: Second Derivative of Inverse Polynomial Function

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Problem 52973. Easy Sequences 45: Second Derivative of Inverse Polynomial Function

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