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Course: Algebra (all content) > Unit 7
Lesson 20: Finding inverse functions (Algebra 2 level)Finding inverse functions
Learn how to find the formula of the inverse function of a given function. For example, find the inverse of f(x)=3x+2.
Inverse functions, in the most general sense, are functions that "reverse" each other. For example, if takes to , then the inverse, , must take to .
Or in other words, .
In this article we will learn how to find the formula of the inverse function when we have the formula of the original function.
Before we start...
In this lesson, we will find the inverse function of .
Before we do that, let's first think about how we would find .
To find , we need to find the input of that corresponds to an output of . This is because if , then by definition of inverses, .
So which means that
Finding inverse functions
We can generalize what we did above to find for any .
To find , we can find the input of that corresponds to an output of . This is because if then by definition of inverses, .
So .
Since the choice of the variable is arbitrary, we can write this as .
Check your understanding
1) Linear function
2) Cubic function
3) Cube-root function
4) Rational functions
5) Challenge problem
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