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Question

# Let R ={(x,y):x,y∈ R,x2+y2≤25}R′={(x,y):x,y∈ R,y≥49x2}then

A

Domain RR=[3,3]

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B

Range RR[0,4]

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C

Range RR=[0,5]

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D

defines a function RR

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Solution

## The correct options are A Domain R∩R′=[−3,3] C Range R∩R′=[0,5] The equation x2+y2=25 represents a circle with centre (0,0) and radius 5 and the equation y =49x2 represents a parabola with vertex (0,0) and focus (0,916). Hence R∩R′ is the set of point indicated in the fig. = {(x,y):−3≤x≤,0≤y≤5} Thus dom R∩R′=[−3,3] and range R∩R′=[0,5]⊃[0,4] Since (0,0) ∈ R ∩R′ and (0, 0) ∈ R ∩R′ Hence ∈ R∩R′ doesn't define a function.

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