inverse of f(x)=x^3+9x+7

Question

hero · Answer

There's two ways to do this

hero · Answer

Actually, satellite might want to help you. He's good at this

anonymous · Answer

i have no idea how to solve i cubic equation.  do you?

hero · Answer

You just find the inverse...

anonymous · Answer

there is a formula but it is tremendously ugly. i was waiting to see the answer

hero · Answer

I've done it before, yes

anonymous · Answer

so idea is you want to solve 
$$y=x^3+9x+7$$ for x or solve 
$$x=y^3+9y+7$$ for y whatever you like.  
suppose y = 5 how would you do it?

hero · Answer

give me a minute or two

anonymous · Answer

are you sure the question isn't 
find 
$$f^{-1}(2)$$ or something more manageable?

anonymous · Answer

F inverse of (7)

hero · Answer

hmmm

anonymous · Answer

aaah that is what i though!  that we can do

anonymous · Answer

@hero take a look at this http://www.wolframalpha.com/input/?i=10%3Dx^3%2Bx%2B7 that was for 10. go to exact form and look at how ugly it is. i didn't think this was easy with a cube.

anonymous · Answer

but with a number we have hope.  what this is really asking is 
"solve for x 
$$x^3+9x+7=7$$ and that is easy enough

hero · Answer

I see

anonymous · Answer

right big ugly mess yes?

anonymous · Answer

yes

anonymous · Answer

but with 
$$f^{-1}(7)$$ we can do it as long as we understand that it just means find the value of x for which 
$$f(x)=7$$

anonymous · Answer

so put 
$$x^3+9x+7=7$$
$$x^3+9x=0$$
$$x(x^2+9)=0$$
$$x=0$$ done.  and you probably could have done it with your eyeballs since the constant is 7

anonymous · Answer

so since 
$$f(0)=7$$ we know 
$$f^{-1}(7)=0$$

hero · Answer

I was trying to find the inverse, but ran into a few problems

anonymous · Answer

i am sure you did!  me too

hero · Answer

Satellite is it possible to go past level 100?

anonymous · Answer

thank you  i was confused

hero · Answer