Main content
Algebra (all content)
Course: Algebra (all content) > Unit 7
Lesson 20: Finding inverse functions (Algebra 2 level)- Finding inverse functions: linear
- Finding inverse functions: quadratic
- Finding inverse functions: quadratic (example 2)
- Finding inverse functions: radical
- Finding inverses of rational functions
- Finding inverse functions
- Finding inverses of linear functions
© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice
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
Want to join the conversation?
- Why are rational functions called "rational"?(16 votes)
- Rational numbers are numbers that can be expressed as a fraction (a ratio) of two integers.
Rational functions are also fractions (ratios) - with polynomials in the numerator and denominator.(27 votes)
- What is the inverse of the function e to the power of x? Or some other exponential function?
Thank you in advance.(9 votes) - How do you find the inverse of y=x+3/3
?(5 votes)- y=(x+3)/3
3y=x+3
3y-3=x
∴x=3y-3(5 votes)
- how do you find the inverse of F(x)= x/(x-1)(2 votes)
- 𝑦 = 𝑥/(𝑥 – 1)
Swap the domain and range:
𝑥 = 𝑦/(𝑦 – 1)
Now solve for the inverse:
𝑥𝑦 – 𝑥 = 𝑦
𝑥𝑦 – 𝑦 = 𝑥
𝑦(𝑥 – 1) = 𝑥
𝑦 = 𝑥/(𝑥 – 1)
So interestingly, this function is its own inverse. Functions like this are called involutions. Comment if you have questions!(10 votes)
- x-1 = -1/y+1, I got stuck on this part, I don't know how to get rid of a fraction with a denominator like that. help me please!(3 votes)
- I assume y+1 is the denominator, not just y?
We take your equation and multiply both sides by y+1. On the right, we get -1(y+1)/(y+1), and the (y+1)'s cancel. So we're left with
(x-1)(y+1)= -1
Now we divide by (x+1), then subtract 1 to isolate y.(2 votes)
- How would you find the inverse of a function where x is greater/less than a specific number? Example problem: Write the inverse of f(x) = 2x+3 where x > 5(2 votes)
- What is the inverse function of f(x)= x*2 - x(3 votes)
- On question number 4, I don't understand why, we subtract x on from the right, instead of subtracting 'xy' from the left. We need to solve for 'x' right?
Can't solve it both ways?(3 votes) - this question is related to FUNCTIONS topic from maths
How to solve f^1(1/2)
when the only information given in the question is
f(x)=3/2x-5(2 votes) - How do you find the inverse with a set of numbers?(2 votes)