Range of the function $$f(x)=$$$$cos$$−$$1$$⁡$$log4$$⁡x−π$$2+$$$$sin$$−$$1$$⁡$$1+x24x$$ is

Question

Range of the function $$f(x)=$$$$cos$$−$$1$$⁡$$log4$$⁡x−π$$2+$$$$sin$$−$$1$$⁡$$1+x24x$$ is

Infinity Learn · Accepted Answer

$$fx=-$$$$sin$$$$-1logx$$ $$4$$ $$+$$$$sin$$$$-11+x24x$$       since $$sin$$$$-1x$$ $$+$$ $$cos$$$$-1x=$$π$$2$$        domain of first function is $$1$$ only  since $$-$$$$sin$$$$-1$$ logx $$4$$ ≥$$0$$     ⇒  $$sin$$$$-1logx$$ $$4$$ ≤ $$0$$     ⇒     logx $$4$$ ≤$$sin0$$      ⇒  logx $$4$$  $$=0$$        ⇒  $$x=1$$              therefore fx domain also $$1$$       since Domain of $$f+g=Domain$$ of f∩Domain of g Range of fx $$=$$ $$f1$$ $$=-$$$$sin$$$$-1$$ $$0$$ $$+$$$$sin$$$$-11+14$$                                      $$=$$$$sin$$$$-112$$                                      $$=$$π$$6$$

$Range of the function f (x) = \sqrt{\cos^{- 1} (\sqrt{\log_{4} x}) - \frac{π}{2}}$ $+ \sin^{- 1} (\frac{1 + x^{2}}{4 x}) is$

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Range of the function f(x)=cos−1⁡log4⁡x−π2+sin−1⁡1+x24x is

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$Range of the function f (x) = \sqrt{\cos^{- 1} (\sqrt{\log_{4} x}) - \frac{π}{2}}$ $+ \sin^{- 1} (\frac{1 + x^{2}}{4 x}) is$