# How To Find The Inverse of a Function | Summary and Q&A

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September 9, 2017
by
The Organic Chemistry Tutor
How To Find The Inverse of a Function

## TL;DR

Learn how to find the inverse of a function by switching variables, isolating the variable, and solving for it.

## Key Insights

• 😀 The inverse of a function can be found by replacing f(x) with y and switching the variables.
• 😀 Isolating the y variable involves performing mathematical operations on both sides of the equation.
• 😀 Solving for y requires applying the appropriate mathematical steps, such as adding, subtracting, dividing, or taking the cube root.
• 🫥 Inverse functions can exist only for functions that pass the horizontal line test.
• 🫚 The process of finding the inverse can be applied to various types of functions, including linear, cubic, square root, and cube root functions.
• 💁 The final answer for the inverse function may be expressed in expanded form or factored form, depending on the situation.
• 💁 Equivalent answers may exist for the inverse function, depending on the form of the equation.

## Transcript

in this video we're going to talk about how to find the inverse of a function so consider the function f of x is equal to two x minus seven what do we need to do the first thing that you should do is replace f of x with y y and f of x basically are the same thing now in your next step switch x with y so x is equal to two y minus seven and then afte... Read More

### Q: What is the first step in finding the inverse of a function?

The first step is to replace f(x) with y and switch the variables by replacing x with y.

### Q: How do you isolate the y variable in the equation?

To isolate the y variable, perform mathematical operations, such as addition or subtraction, on both sides of the equation to isolate y on one side.

### Q: What should be done after isolating the y variable?

After isolating the y variable, the next step is to solve for y by applying the appropriate mathematical steps, such as dividing or taking the cube root.

### Q: Do all functions have an inverse?

Not all functions have an inverse. For a function to have an inverse, it must pass the horizontal line test, meaning that no horizontal line intersects the graph of the function at more than one point.

## Summary & Key Takeaways

• To find the inverse of a function, replace f(x) with y and switch x with y.

• Isolate the y variable by performing mathematical operations to get it on one side of the equation.

• Solve for y by applying the appropriate mathematical steps.

• Examples are provided to demonstrate the process of finding the inverse of different functions.