The range of the functions. Observe the following lists. List $$-$$ I List – II $$A)$$ x $$-$$ [x] $$1)$$ [$$0$$, $$5$$] $$B)$$ $$25$$−$$x2$$ $$2)$$ [$$13$$, $$1$$] $$C)$$ $$12$$−$$cos3x$$ $$3)$$ (0$$, $$5) $$4)$$ $$sin2x$$ $$+$$ $$cos4x$$ $$4)$$ [$$0$$, $$1)$$ $$5)$$ [$$34$$, $$1$$] The correct match for list I from list II

Question

The range of the functions. Observe the following lists.                      List $$-$$ I                                 List – II             $$A)$$   x $$-$$ [x]                                $$1)$$ [$$0$$, $$5$$]             $$B)$$ $$25$$−$$x2$$                               $$2)$$  [$$13$$,  $$1$$]                  $$C)$$ $$12$$−$$cos3x$$                              $$3)$$  (0$$, $$5)             $$4)$$ $$sin2x$$ $$+$$ $$cos4x$$                    $$4)$$  [$$0$$, $$1)$$                                                                 $$5)$$  [$$34$$,  $$1$$]                     The correct  match for list I from list II

Infinity Learn · Accepted Answer

(A)  range of x−[x]$$=$$[$$0$$,$$1$$]                   (B) Range of $$25$$−$$x2=$$[$$0$$,$$5$$]                 (C$$ $$) $$13$$≤$$12$$−$$cos3x$$≤$$1=$$[$$13$$,$$1$$]                 (D) $$sin2x+cos2x(1$$−$$sin2x)$$                             $$=1$$−$$14sin22x$$      Range $$=$$[$$34$$,$$1$$]                     $$4$$, $$1$$, $$2$$, $$5$$

Detailed Solution

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