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Question

If y=f(x), where f:AB is a function in x, then which of the following statements is true?

(i) Every element of A needs to have an image.

(ii) xA must be related to one and only one value of y of B. 



A

Statement (i) is true, but statement (ii) is false.

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B

Statement (ii) is true, but statement (i) is false.

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C

Both statements (i) and (ii) are true.

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D

Neither statement (i) nor statement (ii) is true.

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Solution

The correct option is D

Both statements (i) and (ii) are true.


A relation f from set A to set B is said to be a function if each element of A has one and only one image in B.

Thus, it is necessary for every element of A to have an image in B. It is also necessary that an element of A has a unique image in B.
Thus, both the statements are true.


Mathematics

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