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 $R_1$.
Answer & explanation
Correct answer: option 1
We have,
$R_1$ = {(x, y) | y = 2x + 7, where x ∈ R and -5 ≤ x ≤ 5}
Domain of $R_1 ≡ {-5≤x≤5, x∈ R} ≡ [-5, 5]$
$∵ x ∈ [−5, 5], 2x ∈ [−10, 10]$
$⇒ 2x + 7 ∈ [-3, 17]$
Thus range is [-3, 17].