The domain of the function $$f(x)=$$$$sin$$−$$1$$⁡(3$$−$$x)ln$$⁡$$($$|x|−$$2) is

Question

The domain of the function $$f(x)=$$$$sin$$−$$1$$⁡(3$$−$$x)ln$$⁡$$($$|x|−$$2) is

Infinity Learn · Accepted Answer

fx $$=$$$$sin$$$$-13-xlogx-2$$  let gx $$=$$ $$sin$$$$-13-x$$       then $$-1$$≤$$3-x$$≤$$1$$ ⇒$$1$$≥$$x-3$$≥$$-1$$ ⇒$$4$$≥x≥$$2$$ ⇒  domain of $$gx=$$ $$D1=2$$,$$4$$  let hx $$=logx-2$$   then  $$x-2$$ >$$0$$ ⇒x>$$2$$ ⇒ domain of $$hx=D2=-$$∞,$$-2$$∪$$2$$,∞ ⇒domain of $$fx=$$ $$D1$$∩$$D2-x$$∈$$R/$$ $$hx=0$$                                                      $$=$$ $$(2$$, $$4$$] $$-3$$                  since $$hx=0$$ ⇒ $$x-2=1$$⇒$$x=$$±$$3$$

$The domain of the function f (x) = \frac{\sin^{- 1} (3 - x)}{\ln (| x | - 2)} is$

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The domain of the function f(x)=sin−1⁡(3−x)ln⁡(|x|−2) is

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$The domain of the function f (x) = \frac{\sin^{- 1} (3 - x)}{\ln (| x | - 2)} is$