Domain of the function is y- -cos x-1-2-6-35x-6x2

The correct option is A ∴ D_1∩ D_2= [ 0,π /3 ]∪ [ 5π /3, 6 ] D_1 is given by cos x≥1/2 ∴ 0≤ x≤π/3 ....1st quad.or 5π/3≤ x≤ 2π .. ...

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Standard XII

Mathematics

Continuity in an Interval

Domain of the...

Question

Domain of the function is $y = \frac{\sqrt{cos x - 1 / 2}}{\sqrt{6 + 35 x - 6 x^{2}}}$

∴ D_{1} \cap D_{2} = [0, π / 6] \cup [5 π / 3, 6]

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∴ D_{1} \cap D_{2} = [0, π / 3] \cup [5 π / 3, 6]

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∴ D_{1} \cap D_{2} = [0, π / 3] \cup [5 π / 6, 6]

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∴ D_{1} \cap D_{2} = [0, π / 2] \cup [5 π / 3, 6]

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Solution

The correct option is A $∴ D_{1} \cap D_{2} = [0, π / 3] \cup [5 π / 3, 6]$
$D_{1}$ is given by $cos x \geq \frac{1}{2}$
$∴ 0 \leq x \leq \frac{π}{3}$ ....1st quad.or $\frac{5 π}{3} \leq x \leq 2 π$ ...4th quad., $π = 3.142$
$D_{2} = 6 + 35 x - 6 x^{2} > 0$ or $6 x^{2} - 35 x - 6 < 0$
$(6 x + 1) (x - 6) < 0 ∴ - 1 / 6 < x < 6$
$∴ D_{1} \cap D_{2} = [0, π / 3] \cup [5 π / 3, 6]$

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Domain of the function is y=√cosx−1/2√6+35x−6x2

The correct option is A ∴D1∩D2=[0,π/3]∪[5π/3,6]D1 is given by cosx≥12∴0≤x≤π3 ....1st quad.or 5π3≤x≤2π ...4th quad., π=3.142D2=6+35x−6x2>0 or 6x2−35x−6<0(6x+1)(x−6)<0∴−1/6<x<6∴D1∩D2=[0,π/3]∪[5π/3,6]

Domain of the function is $y = \frac{\sqrt{cos x - 1 / 2}}{\sqrt{6 + 35 x - 6 x^{2}}}$