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

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

Mathematics
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this has to be done algebraically?
yeah, idk how to do it

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i'm not sure how to do the sqrt part along with the y^3 part
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
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.
I was thing a change of variable, but the equations I ended up with weren't much better than this one
i have a suggestion
set \[x^3+\sqrt{x+7}=11\] and solve for \(x\)
you can do it using algebra, but i would not there is a simpler way
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.
since 11 is an integer, \(x+7\) must be a perfect square
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
7+2=9, so 2?
an easy check now right?
\[2^3+\sqrt{2+7}=?\]
8+3=11.. so its really 2 wait that's it??
lol yeah, that's it
oh okay thanks.. it's like a trial and error method then

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