What is an Inverse Function?
In real life, did you ever undo the activity you or some other person has performed? If yes, then you have applied inverse function in your life. The inverse function is a function which will undo another function. For example, let us consider that you have to call your friend using your mobile phone. When you wanted to dial to your friend, you will open the phone book, select his name and click the call button. What happens internally? The phone number of the corresponding name is retrieved and a call is established to that number. In the inverse way, what happens when your friend calls you? You get his name listed in the caller id. This is because; your friend’s phone number reaches your phone. The number gets converted into name and gets displayed. Thus, while calling your friend, the name gets converted into number. While receiving the call, the inverse of function happens and the number gets converted into the name.
However, the inverse of a function must result in the function itself i.e. assume that John is in your contact list and his number is 9904567345. If you call John from your phone book, then the call goes to 9904567345. In that case, when you receive a call back from 9904567345, it should be displayed as John in your phone and not some other name.
Here is another example for you: If a function represents the statement: “John is the father of Dave” then the inverse function will be: “Dave is the son of John”.
How to find Inverse Function?
Now that we know what the inverse of a function is, let us concentrate on how to find inverse function. Finding the inverse of a function can be demonstrated using the algebraic equation x = 4y + 3.
For finding inverse functions of x=4y+3, follow the steps given below:
Step 1: Move the + 3 on right side to the left side. Inverse of addition is subtraction. Thus when the +3 goes to the left side, it becomes -3. Thus the function will be evolved into x-3 = 4y.
Step 2: Now the number 4 has to be moved from right side to left side. Number 4 which is multiplied with y has to move to left side. Inverse of multiplication is division. Thus the 4 on the right hand side will perform division when moving to the left side. The function will now be transformed into (x-3)/4 = y.
Thus the inverse function of x=4y+3 is y=(x-3)/4.
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| Inverse Function |
However, the inverse of a function must result in the function itself i.e. assume that John is in your contact list and his number is 9904567345. If you call John from your phone book, then the call goes to 9904567345. In that case, when you receive a call back from 9904567345, it should be displayed as John in your phone and not some other name.
Here is another example for you: If a function represents the statement: “John is the father of Dave” then the inverse function will be: “Dave is the son of John”.
How to find Inverse Function?
Now that we know what the inverse of a function is, let us concentrate on how to find inverse function. Finding the inverse of a function can be demonstrated using the algebraic equation x = 4y + 3.
For finding inverse functions of x=4y+3, follow the steps given below:
Step 1: Move the + 3 on right side to the left side. Inverse of addition is subtraction. Thus when the +3 goes to the left side, it becomes -3. Thus the function will be evolved into x-3 = 4y.
Step 2: Now the number 4 has to be moved from right side to left side. Number 4 which is multiplied with y has to move to left side. Inverse of multiplication is division. Thus the 4 on the right hand side will perform division when moving to the left side. The function will now be transformed into (x-3)/4 = y.
Thus the inverse function of x=4y+3 is y=(x-3)/4.
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