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Inverses and Radical Functions

Learn how to find the inverse of a polynomial function by restricting its domain. This lesson in College Algebra covers inverse functions and radical functions with practical examples to help you understand and apply the concepts.

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College AlgebraInverses and Radical FunctionsRestrict the domain to find the inverse of a polynomial functionSc far, we have been able t o find the inverse functions c fcubic functionswithout having to restrict their domains. However, as we know, not allcubit polynomials are one-to-one. Some functions that are not one-to-one may have their domain restricted so that they are one-to-one. butonly over that domain. The function over the restricted domain would then have aninverse function.Since quadratic functions are not one-to-one. we must restrict their domain in order to find their inverses.A General Note: Restricting the DomainI f a function is not one-to-one, it cannot have an inverse. If we restrict the domain of the function so that it becomes one-to-one. thus creating anew function, this new function will have an inverse.How Tc: Given a polynomial function, restrict the domain of = function that is not one-to-one and then find the inverse.Restrict the domain by determining a domain on which the original function is one-to-one.Replace flyl with y.niterchangexand y.Solve fory and rename the function or pair of function/Revise the formula for/by ensuring that the outputs of the inverse function correspond to the restricted domain of the original function.Example 3: Restricting the Domain to Find thenverse o f a Polynomial FunctionFind the inverse function of it/ (*) = ( *4)1, x > 4/ ( r )=(u:4)i, a : < 4SolutionThe original function/ ( « ) = ( »4)4is not one-to-one, but the function is restricted to a domain o fi> 4Figure5

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