Inverse of a Domain Restricted Function

In this lesson, we will learn how to find the inverse of a function when the domain is restricted. Additionally, we will learn how to find the inverse of a many-to-one function by imposing a domain restriction. In a many-to-one function, multiple input values can yield the same output value, making it non-invertible over its entire domain. However, by carefully selecting a restricted domain that eliminates the multiple outputs, we can create a one-to-one function and then find our inverse. To impose a domain restriction, we aim to identify a subset of the original domain where the function exhibits a unique output for every input. This can be achieved by carefully considering the characteristics of the function and analyzing its behavior. By excluding specific input values or intervals that lead to non-unique outputs, we create a restricted domain that ensures the function becomes one-to-one. With this restriction in place, we can confidently proceed to find the inverse of the function, as the one-to-one mapping guarantees a unique output for each input, facilitating a well-defined inverse function.