The number of integral elements in the domain of the function $$f(x)=$$$$sin$$−$$1$$⁡$$x2$$−$$2x3+$$[x]$$+$$[−x], where [.]denotes greatest integer function, is

Question

The number of integral elements in the domain of the function $$f(x)=$$$$sin$$−$$1$$⁡$$x2$$−$$2x3+$$[x]$$+$$[−x], where [.]denotes greatest integer function, is

Infinity Learn · Accepted Answer

Given that $$f(x)=$$$$sin$$−$$1$$⁡$$x2$$−$$2x3+$$[x]$$+$$[−x] Now, [x]$$+$$[−x] is defined only for integral values of ' x '    And $$sin$$−$$1$$⁡$$x2$$−$$2x3$$ is defined when −$$1$$≤$$x2$$−$$2x3$$≤$$1$$ If $$x2$$−$$2x3$$≥−$$1$$⇒$$x2$$−$$2x+3$$≥$$0D$$<$$0$$ It has no real values and  $$ifx2$$−$$2x3$$≤$$1$$⇒$$x2$$−$$2x$$−$$3$$≤$$0$$⇒(x+1)(x$$−$$3)≤$$0$$⇒x∈[−$$1$$,$$3$$]∴ Domain of $$f(x)$$ is [−$$1$$,$$3$$]∴x∈$${$$−$$1$$,$$0$$,$$1$$,$$2$$,$$3}$$ $$($$∵ Integralvalues only $$)$$∴ Number of integral elements in the domain are $$5$$

$The number of integral elements in the domain of the function$
$f (x) = \sin^{- 1} (\frac{x^{2} - 2 x}{3}) + \sqrt{[x] + [- x]}, where [.]denotes greatest integer function, is$

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The number of integral elements in the domain of the function f(x)=sin−1⁡x2−2x3+[x]+[−x], where [.]denotes greatest integer function, is

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$The number of integral elements in the domain of the function$
$f (x) = \sin^{- 1} (\frac{x^{2} - 2 x}{3}) + \sqrt{[x] + [- x]}, where [.]denotes greatest integer function, is$