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Home » Is the given relation a function? Give reasons for your answer. (i) g = n, (1/n) |n is a positive integer (ii) s = {(n, n2) | n is a positive integer}
Is the given relation a function? Give reasons for your answer. (i) g = n, (1/n) |n is a positive integer (ii) s = {(n, n2) | n is a positive integer}
CBSE | Class 11 | Maths | NCERT Exemplar | Relations and Functions
Is the given relation a function? Give reasons for your answer. (i) g = n, (1/n) |n is a positive integer (ii) s = {(n, n2) | n is a positive integer}

Solution:

(i) Provided,

\mathrm{g}=\mathrm{n},(1 / \mathrm{n}) \mid \mathrm{n} is a positive integer

As a result, the element n is a positive integer and the corresponding 1/n will be a unique and distinct number.

Hence, in the domain every element has unique image.

If every element of one set has one and only one image in other set then a relation is said to be a function.

As a result, g is a function.

(ii) Provided,

s=\{(n, n 2) \mid n is a positive integer \}

As a result, the element n is a positive integer and the corresponding n^{2} will then be a distinct and unique number, since square of any positive integer is unique.

Hence, in the domain every element has unique image.

If every element of one set has one and only one image in other set then a relation is said to be a function.

As a result, s is a function.

i

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