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in this lesson Ill show you how to find the fixed points of a function lets begin with a bit of theory and this is important to find the fixed points of a function means to find when its input values equal its output values since the equation Y is equal to X is purely a one-to-one function and the reason why its one to one is because any value you put into X you get the exact same output as in your y to find any fixed point for any function we set that function equal to X and solve so I have three examples prepared for you well start with the first one question number one we have find the fixed points of f of x is equal to the cube root of x so all we have to do is set f of x equal to X we have the cube root of x is equal to X remember that the cube root of x is the same thing as x to the power of a third is equal to X we Cube both sides of the equation and when we do that Watch What Happens we get X is equal to X cubed bringing that over we end up with zero is equal to X cubed mi