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CGP EDU Academic Team
Published on: August 13, 2026
Let R = {(x, y): x, y ∈ R , x 2 + y 2 ≤ 25} R ′ = {(x, y): x, y ∈ R , y ≥ x 2 } then
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b, c)
The equation x 2 + y 2 = 25 represents a circle with centre (0, 0) and radius 5 and the equation y = 
x 2 represents a parabola with vertex (0, 0) and focus (0, 5). Hence R ∩ R ′
is the set of points indicated in the fig.
= {(x, y): –3 ≤ x ≤ 3, 0 ≤ y ≤ 5}
Thus dom R ∩ R ′ = [–3, 3]
and range R ∩ R ′ = [0, 5] ⊃ [0, 4]
Since (0, 0) ∈ R ∩ R ′ and (0, 5) ∈ R ∩ R ′
Hence R ∩ R ′ doesn't define a function.
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