Let R - x - y - x - y - R - x 2- y 2- 25 and R - x - y - x - y - R - y -4-9 x 2 thenA- Domain of R - R -3-3-B- Range of R - R -0-4-C- Range of R - R -0-5-D- R - R - defines a function

The correct options are A Domain of R ∩ R'=[ 3,3] C Range of R ∩ R'=[0,5] x^2+y^2 ≤ 25 9y gt; 4x^2 x^2 ≤9/4y x^2=9y/4 9y/4+y^2 25 =0 4y^2+9y 100=0 ...

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Byju's Answer

Standard XII

Mathematics

Using Monotonicity to Find the Range of a Function

Let R = x , y...

Question

Let $R = {(x, y); x, y \in R, x^{2} + y^{2} \leq 25} a n d R^{'} - {(x, y); x, y \in R, y \geq \frac{4}{9} x^{2}}$ then

Domain of

R \cap R^{'} = [- 3, 3]

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Range of

R \cap R^{'} = [0, 4]

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Range of

R \cap R^{'} = [0, 5]

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R \cap R^{'}

defines a function

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Solution

The correct options are
A Domain of $R \cap R^{'} = [- 3, 3]$

C Range of $R \cap R^{'} = [0, 5]$

$x^{2} + y^{2} \leq 25 9 y > 4 x^{2} x^{2} \leq \frac{9}{4} y x^{2} = \frac{9 y}{4} \frac{9 y}{4} + y^{2} - 25 = 0 4 y^{2} + 9 y - 100 = 0 [y - 4] [4 y + 25] = 0 y = 4$
Domain $R \cap R^{'} i s [- 3, 3]$
Range of $R \cap R^{'}$ =[0,5]

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Similar questions

Let R = ${(x, y) : x, y \in R, x^{2} + y^{2} \leq 25} R^{'} = {(x, y) : x, y \in R, y \geq \frac{4}{9} x^{2}}$ then

Q. Let

A = {(x, y); x, y ϵ R, x^{2} + y^{2} \geq 25}

B = {(x, y); x, y ϵ R, 9 y \leq 4 x^{2}}

then

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R

from set

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B = {1, 4, 9, 15}

is defined as :

R = {(x, y) \in R : x = \sqrt{y}},

then

Q. If R = {(x, y) : x, y ∈ Z, x² + y² = 25}, then Domain (R) = .................... and Range (R) = __________.

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\in

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

The correct options are A Domain of R∩R′=[−3,3] C Range of R∩R′=[0,5] x2+y2≤259y>4x2x2≤94yx2=9y49y4+y2−25=04y2+9y−100=0[y−4][4y+25]=0y=4 Domain R∩R′is[−3,3] Range of R∩R′ =[0,5]

Let $R = {(x, y); x, y \in R, x^{2} + y^{2} \leq 25} a n d R^{'} - {(x, y); x, y \in R, y \geq \frac{4}{9} x^{2}}$ then