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Inverse Of A Function




 
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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?

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) = 2x + 3

b) g(x) = – 5

c) h(x) =

Solution:

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




Video

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


 

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