How do I find the inverse(f^-1) of the function f(x)=1-2x-x^3? (Will give medals)

Question

anonymous · Answer

The way I like to do it is by writing "f(x)" as "y"... 

y = (2x-3)/(x+1) 

And then switching your x's and your y's... 

x = (2y-3)/(y+1) 

and solving for y again. 

So... 

multiply both sides by (y+1): 

x(y+1) = (2y-3) 

xy + x = 2y - 3 

get everything on one side (in this case, subtract (2y - 3) from both sides): 

xy + x - 2y + 3 = 0 

Now, group your y's together, because remember, we want our answer to be y = ... 

xy - 2y + x + 3 = 0 

Group and factor: 

y(x-2) + x + 3 = 0 

Isolate y by moving all your x's to the one side (so subtract (X + 3) from both sides): 

y(x-2) = - x - 3 

Divide both sides by (x - 2): 

y = - (x+3)/(x-2) 


And remember, the y in this equation is actually your inverse, so: 

The inverse is 

f '(x) = - (x+3)/(x-2) 
@Matthew071

anonymous · Answer

I understand the inverse concept I just need help finding the inverse of
$$f(x)=1-2x-x^3$$