As soon as you're given f(x), you can find its derivative . You also need to find the inverse of f evaluated at 6: by inspection.
Now you just plug that information into your equation to get the answer.
To find , you need to find a value for x that makes y equal to 6. That is, you need to find the solution for .
Notice that the coefficients of f(x) add up to 6. Knowing this, all you have to do is plug in x=1 to make the x's "disappear":
A general way to solve this type of problem is to use synthetic division to factor the polynomial: