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Definition of Inverse - Problem 3

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We know that in order to find the inverse of a function algebraically, we need to swap x and y and then solve for y. In doing this, the domain and range get swapped, as well. We can see this graphically as a function and its inverse are reflected across the line y = x. When working with radical functions in particular, we need to make sure that whatever is under the radical, called the radicand, is always greater than or equal to zero. This will help us verify that the domain and range have been swapped. To check our work, we need to use composition of functions to show that f(f-1(x)) = f-1(f(x))= x .

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