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Let F Be the Subset Of Z × Z Defined By F = {(Ab, A + B): A, B ∈ Z}. Is F A Function From Z To Z: Justify Your Answer. - CBSE (Arts) Class 11 - Mathematics

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Question

Let f be the subset of Z × Z defined by = {(aba + b): ab ∈ Z}. Is f a function from Z to Z: justify your answer.

Solution

The relation f is defined as = {(aba + b): ab ∈ Z}

We know that a relation f from a set A to a set B is said to be a function if every element of set A has unique images in set B.

Since 2, 6, –2, –6 ∈ Z, (2 × 6, 2 + 6), (–2 × –6, –2 + (–6)) ∈ f

i.e., (12, 8), (12, –8) ∈ f

It can be seen that the same first element i.e., 12 corresponds to two different images i.e., 8 and –8. Thus, relation f is not a function.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 2: Relations and Functions
Ex. 2.40 | Q: 11 | Page no. 47

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Solution Let F Be the Subset Of Z × Z Defined By F = {(Ab, A + B): A, B ∈ Z}. Is F A Function From Z To Z: Justify Your Answer. Concept: Functions.
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