Let $$f(x)=2$$π$$($$$$sin$$−$$1$$[x]$$+$$$$cot$$−$$1$$[x]$$+$$$$tan$$−$$1$$[x]$$)where$$ [x]denotes greatest integer function less than equal to x. If A and B denotes the domain and Range of $$f(x)respectively$$, then the number of integers in A∪B is

Question

Let  $$f(x)=2$$π$$($$$$sin$$−$$1$$[x]$$+$$$$cot$$−$$1$$[x]$$+$$$$tan$$−$$1$$[x]$$)where$$ [x]denotes greatest integer function less than equal to x.  If A and B denotes the domain and Range of  $$f(x)respectively$$, then the number of integers in A∪B is

Infinity Learn · Accepted Answer

Given $$fx=2$$$$π$$$$sin$$$$-1x+$$$$cot$$$$-1x+$$$$tan$$$$-1x$$ $$sin$$$$-1$$ domain is $$-1$$,$$1$$, $$cot$$$$-1$$ and $$tan$$$$-1$$ domain is $$-$$∞,∞. ∴The domain of fx is [$$-1$$,$$2)$$.   ∵if x∈ [$$-1$$,$$2)$$, then x can take $$-1$$,$$0$$,$$1$$ only  ∴$$A=$$[$$-1$$,$$2)$$ Now if x∈[$$-1$$,$$0)$$, then $$x=-1$$  ⇒ $$fx=2$$π$$-$$π$$2+3$$$$π$$$$4-$$π$$4=0$$ for  x∈[$$0$$,$$1)$$, then $$x=0$$ ⇒  $$fx=2$$$$π$$$$0+$$π$$2+0=1$$ for  x∈[$$1$$,$$2)$$, then $$x=1$$ ⇒$$fx=2$$ππ$$2+$$π$$4+$$π$$4=2$$ ∴range of $$fx=B={0$$,$$1$$,$$2}$$ ∴A∪$$B=$$[$$-1$$,$$2)$$∪$${0$$,$$1$$,$$2}=-1$$,$$2$$ ∴The number of integers in A∪B is $$4$$

Properties of ITF

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Let $f (x) = \frac{2}{π} (\sin^{- 1} [x] + \cot^{- 1} [x] + \tan^{- 1} [x])$ where $[x]$ denotes greatest integer function less than equal to $x$ . If A and B denotes the domain and Range of $f (x)$ respectively, then the number of integers in $A \cup B$ is

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Properties of ITF

Remember concepts with our Masterclasses.

Let f(x)=2π(sin−1[x]+cot−1[x]+tan−1[x])where [x]denotes greatest integer function less than equal to x. If A and B denotes the domain and Range of f(x)respectively, then the number of integers in A∪B is

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Let $f (x) = \frac{2}{π} (\sin^{- 1} [x] + \cot^{- 1} [x] + \tan^{- 1} [x])$ where $[x]$ denotes greatest integer function less than equal to $x$ . If A and B denotes the domain and Range of $f (x)$ respectively, then the number of integers in $A \cup B$ is