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A function f : X→ Y is said to be Inverse function if,

A function f : X→ Y is said to be Inverse function if, Correct Answer f<sup>-1</sup>(y) = x

Concept:

If f : X→ Y is one-one onto function, then the pre-image of y € Y is called the Inverse image of y under the function f.

The function f : Y→ X which associates to each y € Y its inverse image x € X given by f(x) = y, is called the inverse function of f : X→Y.

Clearly, f-1 (y) = x ⇔ f(x) = y, y € Y, x € X.

Additional Information

It should be noted that the inverse function of f : X→ Y is defined only when f is one-one onto. Further, if an inverse function  f-1 : Y→ X exists, then it is also one-one onto.

Related Questions

The following sentences form a paragraph. These four parts are numbered as P, Q, R and S. They are not given in their proper order. Read the sentences and choose the alternative that arranges them in correct order. P. Inverse problem refers to the scientific problem of estimating the different causes that led to a particular outcome.  Q. This is in contrast to the forward or the direct problem where scientists try to find the outcome that results from a series of causes. R. A scientist observing a photograph, for instance, would be faced with the inverse problem while trying to figure out the various causal factors that combined to form the final photograph. The inverse problem is applied to understand processes in a wide variety of sciences. S. Scientists trying to understand an observation may at times have to work backwards to estimate the causal factors behind it.
In a town fair 50 people were asked which dessert they liked: ice cream, Donuts, or cupcakes. 28 said they like ice cream, 26 said they like donuts, and 26 said they like cupcakes. 8 said they like all three. 17 said they like donuts and cupcakes, 11 said they like ice cream and cupcakes. 5 said they do not like any of these. Find those people who liked ice cream and donuts but not cupcakes.
If 'banana' is said 'apple', 'apple' is said 'grapes', 'grapes' is said 'mango', 'mango' is said 'cashew', 'cashew' is said 'guava', 'guava' is said 'papaya' then which fruit is known as the king of fruits?
S1: A man handed a pair of trousers to the departmental store-clerk and said,"I'd like these altered, please".
P: He said that free alteration is not possible without a receipt.
Q: The man said,"Okay, I'd like to return the trousers". The clerk took them back and returned his money.
R: The man pushed the money and said,"Now I want to buy them". The clerk put the trousers in a bag, issued receipt and handed him both.
S: The clerk asked for the sales receipt but after searching his pockets the man replied that he had lost it.
S6: Triumphantly he put the trousers and the receipt on the counter and said,'I'd like to have these altered, please."

The Proper sequence should be:
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