If $R_1$ = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of $R_1$.

Home » If = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of .

If $R_1$ = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of $R_1$ .

If $R_1$ = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of $R_1$ .

Solution:

Provided,

$R_1$ $=\{(x, y) \mid y=2 x+7$ , in which x ∈R and ${-} 5\leq x\leq 5}$ is a relation

All the first elements of all the ordered pairs of $R_1$ , i.e., x, are included in the domain of $R_1$

Also provided $-5 \leq x \leq 5$ .

As a result,

Domain of $R_1$ $= [{-}5, 5]$

All the second elements of all the ordered pairs of $R_1$ , i.e., y, are included in the range of R.

Also provided y $= 2x + 7$

So now, $\mid x \in[-5,5]$

Now multiply both L.H.S. and R.H.S. by 2,

We have,

$2 \times \in[-10,10]$

Now add L.H.S. and R.H.S. with 7,

We have,

$2 x+7 \in[-3,17$

Or, $y \mid \in[-3,17]$

Therefore,

Range of $R_1$ $= [{-}3, 17]$

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