help, I'm stuck with the question below. About Inverse Function. I just need help getting the inverse of the function.

Question

owlet · Answer

attachment

anonymous · Answer

this has to be done algebraically?

owlet · Answer

yeah, idk how to do it

owlet · Answer

i'm not sure how to do the sqrt part along with the y^3 part

anonymous · Answer

not really sure how to go about solving the equation for y, but they're basically asking you to find where y = 11. I graphed it and backed out a solution that way. not exactly efficient

owlet · Answer

i tried doing that also. 
First I planned to solve  the value of x when f(x)=11 , so that I could just switch it. 
But I'm stuck. We're not allowed to use any devices during exams/tests/quizzes, so I wanted to learn how to do this.

anonymous · Answer

I was thing a change of variable, but the equations I ended up with weren't much better than this one

anonymous · Answer

i have a suggestion

anonymous · Answer

set $$x^3+\sqrt{x+7}=11$$ and solve for $x$

anonymous · Answer

you can do it using algebra, but i would not 
there is a simpler way

owlet · Answer

as i've said before, that's the first thing I tried.

sqrt(x+7)=11-x^3
then if I square both sides,I will still get a not so good set up which confused me.

anonymous · Answer

since 11 is an integer, $x+7$ must be a perfect square

anonymous · Answer

think of a number (gotta be pretty small) that when added to 7 gives a perfect square
you will probably get it on the first try

owlet · Answer

7+2=9, so 2?

anonymous · Answer

an easy check now right?

anonymous · Answer

$$2^3+\sqrt{2+7}=?$$

owlet · Answer

8+3=11.. so its really 2

wait that's it??

anonymous · Answer

lol yeah, that's it

owlet · Answer

oh okay thanks.. it's like a trial and error method then