Find f^-1. f(x)=4+3 √(x-1), x ≥1

Name: Problem 57, Chapter 7: Calculus: One Variable
Uploaded: 2021-08-21T07:12:44-08:00
Duration: 1 min 53 s
Channel: Adrian Co
Description: Find f^-1. f(x)=4+3 √(x-1), x ≥1

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Key Concepts

Inverse Functions

An inverse function reverses the mapping of the original function, meaning that if a function f maps an input x to an output y, then the inverse function f?¹ maps y back to x. The process of finding the inverse involves algebraically solving the equation for x in terms of y and then swapping the variables.

Domain and Range Considerations

When finding an inverse function, it is essential to consider the original function's domain and range because these sets swap roles in the inverse function. The domain of the original function becomes the range of the inverse function, and the range of the original function becomes the domain of the inverse.

Algebraic Manipulation with Radical Expressions

For functions that include radical expressions, finding the inverse often requires isolating the radical term and then eliminating it by raising both sides of the equation to the power that corresponds to the radical. This careful manipulation ensures the correct inverse is obtained while respecting the domain restrictions imposed by the radical.

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