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If R = [(X, Y) : X, Y ∈ W, 2x + Y = 8], Then Write the Domain and Range of R.

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Question

If R = [(xy) : xy ∈ W, 2x + y = 8], then write the domain and range of R.

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Solution

R = {(xy) : xy ∈ W, 2x + y = 8}

\[\text{ As} y = 8 - 2x\]

\[\text{ For }  x = 0, y = 8\]

\[\text{ For}  x = 1, y = 6\]

\[\text{ For } x = 2, y = 4\]

\[\text{ For}  x = 3, y = 2\]

\[\text{ For}  x = 4, y = 0\]

\[\text { For }  x = 5, y < 0\]

\[\text{ So, } y < 0 \text{ for all }  x > 5\]

∴ Domain (R) = {0,1,2,3,4} and Range (R) = {0,2,4,6,8}

 

 

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Chapter 2: Relations - Exercise 2.4 [Page 25]

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R.D. Sharma Mathematics [English] Class 11
Chapter 2 Relations
Exercise 2.4 | Q 10 | Page 25

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