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CBSE Class 12 · 2014 · Relations And Functions XIIVery Short Answer

If

R = {(x, y) : x + 2 y = 8}

is a relation on

N

, write the range of

R

.

Answer: Range $= {1, 2, 3}$

Solution

From

x + 2 y = 8

we get

y = \frac{8 - x}{2} = 4 - \frac{x}{2}

, and both

x, y

must be natural numbers.

x

must be even and keep

y \geq 1

, so

x \in {2, 4, 6}

.

x = 2 \Rightarrow y = 3, x = 4 \Rightarrow y = 2, x = 6 \Rightarrow y = 1

.
The range is the set of attained

y

-values.

Range = {1, 2, 3}

CBSE Class 12 Board · 2014 · Subjective

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