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Relation — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRelation1 Mark
Question
Let $\text{R}=\{(\text{x, y}):\text{x, y}\in\text{Z},\text{y}=2\text{x}-4\}.$ If (a, -2) and $(4,\text{b}^2)\in\text{R},$ then write the values of a and b.
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Answer

We have, $R=\{(x, y): x, y \in Z, y=2 x-4\}$ Now, $y=2 x-4$ Putting $y=-2$ and $x=a$, we get $-2=2 a-4=4-2$ $=2 a \Rightarrow 2=2 a \Rightarrow 2 a=2 \Rightarrow a=\frac{2}{2}=1$ Putting $y=b^2$ and $x=4$, we get $b^2=2 \times 4-4 \Rightarrow b^2=8-4 \Rightarrow b^2=4$ $\Rightarrow \mathrm{b}= \pm 2$ Hence, $\mathrm{a}=1, \mathrm{~b}= \pm 2$

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