The domain of the function $$fx=sinx+cosx+7x-x2-6$$ is

Question

The domain of the function $$fx=sinx+cosx+7x-x2-6$$ is

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We  have  $$fx=sinx+cosx+7x-x2-6$$                                  $$=2sin$$$$π$$$$4+x+7x-x2-6$$     fx    is    defined   if  i    $$7x-x2-6$$≥$$0$$      $$x2-7x+6$$≤$$0$$          ⇒$$1$$≤x≤$$6$$                         (1)ii$$    $$sin$$$$π$$$$4+x$$≥$$0$$                $$x+$$π$$4$$∈........$$-2$$π,$$-$$π∪$$0$$,π∪$$2$$π,$$3$$π.....  ⇒x∈.....$$-$$π$$4$$,$$3$$$$π$$$$4$$∪$$7$$$$π$$$$4$$,$$11$$$$π$$$$4$$....                                                                        $$(2)  From  $$1and2$$,   we  get  x∈$$1$$,$$3$$$$π$$$$4$$∪$$7$$$$π$$$$4$$,$$6$$

The domain of the function fx=sinx+cosx+7x-x2-6 is

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