The domain of the $$functionf(x)=$$$$sin$$−$$1$$⁡$$log2$$⁡$$12x2$$ is

Question

The domain of the $$functionf(x)=$$$$sin$$−$$1$$⁡$$log2$$⁡$$12x2$$ is

Infinity Learn · Accepted Answer

For f (x) to be defined, we must have−$$1$$≤$$log2$$⁡$$12x2$$≤$$1$$⇒$$2$$−$$1$$≤$$12x2$$≤$$21$$ [∵the $$base=2$$>$$1$$]⇒$$1$$≤$$x2$$≤$$4$$                ........ (1)  Now,  $$1$$≤$$x2$$⇒$$x2$$−$$1$$≥$$0$$ i.e. (x$$−$$1)(x+1)≥$$0$$ ⇒ x≤−$$1$$ or x≥$$1$$      ........ (2)  Also, $$x2$$≤$$4$$⇒$$x2$$−$$4$$≤$$0$$ i.e. (x$$−$$2)(x+2)≤$$0$$ ⇒−$$2$$≤x≤$$2$$              ........ (3)From$$ Eq. $$(2) and (3), we get the domain of $$f=(($$−∞,−$$1$$]∪[$$1$$,∞$$))$$∩[−$$2$$,$$2$$] $$=$$[−$$2$$,−$$1$$]∪[$$1$$,$$2$$]

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

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The domain of the functionf(x)=sin−1⁡log2⁡12x2 is

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