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More Lessons for Algebra, Math Worksheets

We have learned that a function f maps*x *to f(*x*).

The inverse of f is a function which maps f(*x*) to *x* in reverse.

The inverse of the function f is denoted by f^{-1}.

The inverse of a function is found by interchanging its range and domain. The domain of*F* becomes the range of the inverse and the range of *F* becomes the domain of the inverse of *F*. The inverse of a function is not always a function and should be checked by the definition of a function. A function only has an inverse if it is one-to-one.

**How to get the inverse of a function?**

### Video

Inverse of a Function

Learn how to find the inverse of a function, step by step example.
Finding the Inverse of a Function

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Algebra, Math Worksheets

We have learned that a function f maps

The inverse of f is a function which maps f(

The inverse of the function f is denoted by f

The inverse of a function is found by interchanging its range and domain. The domain of

The steps involved in getting the inverse of a function are:

**Step 1:**. Replace f(*x*) with *y*

**Step 2: ** Move *y* to the right side of the equation

**Step 3:** Make *x* the subject of the equation

**Step 4: **Replace *x* by f-1(x) and replace *y* by *x*

The following example illustrates these steps.

* Example: *

Find the inverse of each of the following functions:

a) f(*x*) = 2*x* + 3

b) g(*x*) = – 5

c) h(*x*) =

* Solution: *

a) Rewrite f(*x*) = 2*x* + 3 as *y* = 2*x* + 3.

Learn how to find the inverse of a function, step by step example.

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You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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