Let R be a relation in N defined as R - x- y - N - N - x - 2y - 39 Find the domain- co-domain and range of R- Also write R-1 in roster form-

x+2y=39 ⇒ y=39 x2 Since #160; y∈ N,y gt; 0 39 x2 gt;0 39 x gt;0 x lt;39 Since x∈ N,x can take values ={ 1,2,. ...

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Standard IX

Mathematics

Universal Set

Let R be a ...

Question

Let $R$ be a relation in $N$ defined as $R = {(x, y) \in N \times N : x + 2 y = 39}$ Find the domain, co-domain and range of $R$ . Also write $R^{- 1}$ in roster form.

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Solution

$x + 2 y = 39$

$\Rightarrow y = \frac{39 - x}{2}$

Since $y \in N, y > 0$

$\frac{39 - x}{2} > 0$

$39 - x > 0$

$x < 39$

Since $x \in N, x$ can take values $= {1, 2, . . . .38}$

Domain of R $= {1, 2, . . . .38}$

Range of R is $y = \frac{39 - x}{2}, f o r x = {1, 2, . . . .38}$

Range of R $= {1, 2, . . . ., 37}$

when $x = 1, y = 19$

when $x = 2, y = 18.5$

when $x = 37, y = 1$

Domain of f $= {1, 2, . . . .38}$

Range of f $= {1, 2, . . . .37}$

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Let R be a relation in N defined as R={(x,y)∈N×N:x+2y=39} Find the domain, co-domain and range of R. Also write R−1 in roster form.

x+2y=39⇒y=39−x2Since y∈N,y>039−x2>039−x>0x<39Since x∈N,x can take values ={1,2,....38}Domain of R ={1,2,....38}Range of R is y=39−x2,forx={1,2,....38}Range of R ={1,2,....,37}when x=1,y=19when x=2,y=18.5when x=37,y=1Domain of f ={1,2,....38}Range of f ={1,2,....37}

Let $R$ be a relation in $N$ defined as $R = {(x, y) \in N \times N : x + 2 y = 39}$ Find the domain, co-domain and range of $R$ . Also write $R^{- 1}$ in roster form.