Learn how to algebraically find the inverse of a linear function. Understand the relation between the domain and range of the linear function, and how it swaps for the inverse.

To find the inverse function of a given linear function, we switch the independent variable (e.g., [latex]x[/latex]) to [latex]y[/latex] so that it becomes the dependent variable, and the dependent variable (e.g., [latex]y=f(x)[/latex]) to [latex]x[/latex] to become the independent variable.

Nov 16, 2022 · Here is a set of practice problems to accompany the Inverse Functions section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University.

Inverse functions are functions which reverse or “undo” another function. To write the inverse of the function f , we use the notation f^ {-1} . We have seen how to use a function machine to work backwards to find the input from a known output.

Solve real-life problems using inverse functions. You have used given inputs to fi nd corresponding outputs of y f(x) = for various types of functions. You have also used given outputs to fi nd corresponding inputs.

If this inverse relation also qualifies as a function, it's termed an 'inverse function'. The lesson provides a step-by-step guide on how to determine if two functions are inverses of each other, both algebraically and graphically.

An inverse function reverses the operation done by a particular function. In other words, whatever a function does, the inverse function undoes it. In this section, we define an inverse function formally and state the necessary conditions for an inverse function to exist.

For example, find the inverse function for f (𝑥) = 5𝑥 – 2. Step 1. Replace the ‘f (x)=’ in the equation with ‘y=’. We write f (𝑥) = 5𝑥 – 2 as y = 5𝑥 – 2. Step 2. Replace every x in the equation with a y and the y with an x. We switch the 𝑥 for a y and the y for an 𝑥 so that the equation y = 5𝑥 – 2 becomes 𝑥 …

Find the inverse of a linear function. Determine if two functions are inverses by finding f (f −1(x)) f (f − 1 (x)) and f −1(f (x)) f − 1 (f (x)). Graph a linear function and its inverse on the same axes. Recall that in a function, the input value must have one and only one value for the output.

• The inverse of a linear function is the reverse of the original function. It undoes what the original has done and can be found using the inverse operations of the original function in reverse order. For example, to apply the function defined by. f (x) = 3x + 4, multiply x by 3 and then add 4.