Find the inverse relation R^ -1 in the following case: R= (x, y):… - Vidyadip

Question

Find the inverse relation $R^{-1}$ in the following case: $\text{R}=\{(\text{x, y}):\text{x},\text{ y}\in\text{N},\text{ x}+2\text{y}=8\}$

✓

Answer

We have, $\text{R}=\{(\text{x, y}):\text{x},\text{ y}\in\text{N},\text{ x}+2\text{y}=8\}$ Now, x + 2y = 8 ⇒ x = 8 - 2y Putting y = 1, 2, 3 we get x = 6, 4, 2 respectively. For y = 4, we get $\text{x}=0\notin\text{N}$ Also for $\text{y}>4,\text{ x}\notin\text{N}$ $\therefore\ \text{R}=\{(6,1),(4,2),(2,3)\}$ Thus, $\text{R}^{-1}=\{(1,6),(2,4),(3,2)\}$ $\Rightarrow\text{R}^{-1}=\{(3,2),(2,4),(1,6)\}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from Relation→Relation — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Prove that: $\sin^2\frac{2\pi}{5}=\sin^2\frac{\pi}{3}=\frac{\sqrt{5}-1}{8}$

If $f: R \rightarrow R$ be defined by $f(x)=x^2+1$, then find $f^{-1}\{17\}$ and $f^{-1}\{-3\}$.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): $\frac{1+\frac{1}{\text{x}}}{1-\frac{1}{\text{x}}}$

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$ to the ends of its latus rectum.

Find the ratio in which the line segment joining the points (4, 8, 10) and (6, 10, -8) is divided by the yz-plane.

Find the domain of the function $f(x) = \frac{{{x^2} + 2x + 1}}{{{x^2} - 8x + 12}}$.

Find the general solutions of the following equations: $\cos3\text{x}=\frac{1}{2}$

Prove that: $\sin\frac{10\pi}{3}\cos\frac{13\pi}{6}+\cos\frac{8\pi}{3}\sin\frac{5\pi}{6}=-1$

Prove that: $\cos24^\circ\cos55^\circ+\cos125^\circ+\cos204^\circ+\cos300^\circ=\frac12$

Find the value of the following trigonomentric ratio: $\tan\Big(\frac{7\pi}{4}\Big)$