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what is inverse of given function Y=X


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an Inverse Operation reverses the effect of an operation (an operation is a procedure such as addition or multiplication) and gets you back to the number you started with.

what is inverse of given function

Y=X

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Feb 24, 2010
Inverse Functions - Inverse Operations
by: Staff

The problem


what is inverse of given function
Y=X


The solution

Before I answer your question, think about an inverse function this way: it is similar to a reverse listing of a phone book.

A function: The phone number is a function of a person’s name. You have the person’s name; you need to find the phone number.

Normally, to look up a number in a phone book, you start with a name. Names are listed in alphabetical order so you can find a name easily.

For example, imagine looking up the name “John Doe”. Right next to the name “John Doe” is the phone number belonging to “John Doe”. As an example, let’s say the number is (925) 689-5555.

Now imagine yourself looking up another name: “Jim Smith”. Right next to the name “Jim Smith” is the phone number belonging to “Jim Smith”. As an example, let’s say the number for “Jim Smith” is (925) 722-5155.


. . . And so on . . .

The phone numbers listed in a normal phone directory are a function of a person’s name. Look up a name; obtain the phone number for that person.




Inverse Function: you have the phone number; you just don’t know the person’s name.


Now imagine a phone book which lists the phone numbers in numerical order (called a reverse directory), rather than the names in alphabetical order.

You want to know: who is the person with the phone number (925) 689-5555. You look up the phone number, and find the person listed beside the phone number is “John Doe”.

. . . And so on . . .




Now apply this concept to your problem:

Y is a function of X: Y = X

To find the inverse function, solve for X.

The inverse function is: X = Y


Another example: Now, let’s make the problem a little more complicated to illustrate the point.

Find the inverse function for: Y = 2X

What is the inverse function?

Solve for X

The inverse function is: X = Y/2



A final note:

Why would anyone need to know this?

Because . . . Inverse operations are important keys which are used to simplify equations. For more information, see
http://www.solving-math-problems.com/inverse-property.html



Staff
www.solving-math-problems.com



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