Section 1.5 Inverses of Functions

The original function The inverse of the original function

Example1 Given Write the equation for the inverse relation by interchanging the variables and transforming the equation so that y is in terms of x. Plot the function and its inverse on the same screen, using equal scales for the two axes. Explain why the inverse relation is not a function. Plot the line y = x on the same screen. How are the graph of the function and its inverse relation related to this line?

Example 2 Plot the graph of for x in the domain and its inverse using parametric equations (Domain and range of both?)

Example 3 Let Find the equation of the inverse of f. Plot function f and its inverse on the same screen. Is f an invertible function? Why or why not? Quick test - horizontal line test Note: invertible functions are called one-to-one functions. These are functions that are strictly increasing or strictly decreasing. Show algebraically that the composition of with is

Definitions and Properties: Function Inverses The inverse of a relation in two variables is formed by interchanging the two variables. If the inverse of function f is also a function, then f is invertible. If f is invertible and then you can write the inverse of f as To plot the graph of the inverse of a function, either Interchange the variables, solve for y, and plot the resulting equation(s), Or Use parametric mode

If f is invertible, then the compositions of are and provided x is in the domain of f and is in the domain of provided x is in the domain of and is in the domain of A one-to-one function is invertible. Strictly increasing or strictly decreasing functions are one-to-one functions.

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