CPhill

Good answer, rosala...!!!

Nice use of number line graphics there, Melody...!!!!

What progam did you create that with???

I haven't looked at that one, yet...!!!

I'd have been happier if there had actually been a logical question to solve....but, as is, it is an impressive  piece of "art"......LOL!!!

Every perfect number found, so far, is even.....the better question is....."Are there any odd perfect numbers??".....it is speculated that there aren't.......but it hasn't been proved ...!!!

[ BTW...for those that don't know...a perfect number is one that equals the sum its proper divisors...6 is the first one and 28 is the next ]

I did this the same as you and found....as you did...that whatever values were put into the original function to produce "6" - namely, ±√3 and 2 -  were outside the prescribed domain of the original function...!!!!

Maybe we have "clunker" here ?????

If x ≠ 0, what is the solution to the following equation? (1 - x)/x + 2 = 7/x

Getting a common denominator on the left, we have

(1 - x)/x + 2x/x  = 7/x    subtract 2x/x from both sides

(1 -x)/ x  = 7/x - 2x/x

(1-x )/x  = (7 - 2x) /x     cross-multiply

x(1 - x)  = x(7 - 2x)    simplify

x - x^2  = 7x - 2 x^2  rearrange

x^2 - 6x = 0  factor

x(x -6) = 0     set both factors = 0...so x = 0 or  x = 6

And since x can't = 0,   then x = 6 

                      -

Melody...I don't think it's going to be very easy to "manually" isolate  "x" in the function -x^3 -2x^2 + 3x so that an inverse an be found  ..!!!!

Here's what WolfamAlpha generated as the inverse.....it looks pretty  "nasty".... (to say the least)

I think Alan answered this one.....but he did it graphialy, as I recall....