Part of the domain of the function $$f(x)=$$$$cos$$⁡x−$$1/26+35x$$−$$6x2$$ lying in the interval [–$$1$$, $$6$$] is

The function f is meaningful only if $$cos$$ $$x-1/2$$≥$$0$$ , $$6+35x$$ $$6x2$$ >$$0$$ or $$cos$$ x $$-1/2$$≤$$0$$, $$6+35x$$ $$6x2$$ $$0$$ or $$cos$$⁡x≤$$1/2$$,(6$$−$$x)(1+6x)<$$0$$ These inequalities are satisfied if x∈$$($$−$$1/6$$,π$$/3$$]∪[$$5$$π$$/3$$,$$6)$$

Part of the domain of the function $$f(x)=$$$$cos$$⁡x−$$1/26+35x$$−$$6x2$$ lying in the interval [–$$1$$, $$6$$] is

Correct option is 1[−1/6,π/3]∪[5π/3,6]

Questions

Part of the domain of the function $f (x) = \sqrt{\frac{\cos x - 1 / 2}{6 + 35 x - 6 x^{2}}}$ lying in the interval [–1, 6] is

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[−1/6,π/3]∪[5π/3,6]

(–1/6, p/3] » [5p/3, 6)

(–1/6, 6)

none of these

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detailed solution

Correct option is A

The function f is meaningful only if cos x-1/2≥0 , 6+35x 6x2 >0 or cos x -1/2≤0, 6+35x 6x2<0 i. e. , cos x ≥1/2, (6-x)(1+6x)>0 or cos⁡x≤1/2,(6−x)(1+6x)<0 These inequalities are satisfied if x∈(−1/6,π/3]∪[5π/3,6)

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