Question Number 115022 by dw last updated on 23/Sep/20
![[Q.1 ] Find the domain of f(x)=((⌊cos^(−1) (x^4 )⌋+∣⌊x−2tan^(−1) (x)⌋∣+(√(sin(lnx))))/({3x^2 −7}+a^(√(sin(x)+3cos(x))) +ln cos((1/( (√(−x^2 ))))))) where {x} reprents the fractionare part of x: A) ]−2, (√2)[ B) ]0,2[ C) ]−1, 1 [ D) ]−2, −(√2) Explanation please!](Q115022.png)
$$\left[\boldsymbol{{Q}}.\mathrm{1}\:\right]\:\:\:{Find}\:{the}\:{domain}\:{of} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{f}\left({x}\right)=\frac{\lfloor{cos}^{−\mathrm{1}} \left({x}^{\mathrm{4}} \right)\rfloor+\mid\lfloor{x}−\mathrm{2}{tan}^{−\mathrm{1}} \left({x}\right)\rfloor\mid+\sqrt{{sin}\left({lnx}\right)}}{\left\{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{7}\right\}+{a}^{\sqrt{{sin}\left({x}\right)+\mathrm{3}{cos}\left({x}\right)}} +{ln}\:{cos}\left(\frac{\mathrm{1}}{\:\sqrt{−{x}^{\mathrm{2}} }}\right)} \\ $$$${where}\:\left\{{x}\right\}\:{reprents}\:\:{the}\:{fractionare}\:{part}\:{of}\:{x}: \\ $$$$ \\ $$$$\left.{A}\left.\right)\left.\:\left.\right]\left.−\mathrm{2},\:\sqrt{\mathrm{2}}\left[\:\:\:\:\:\:\:{B}\right)\:\:\right]\mathrm{0},\mathrm{2}\left[\:\:\:\:\:\:{C}\right)\:\right]−\mathrm{1},\:\mathrm{1}\:\left[\:\:\:\:{D}\right)\:\right]−\mathrm{2},\:−\sqrt{\mathrm{2}} \\ $$$$ \\ $$$$\:\:\:\:\:\:{Explanation}\:{please}! \\ $$
Answered by Olaf last updated on 23/Sep/20
$$\mathrm{impossible}\:! \\ $$$$\frac{\mathrm{1}}{\:\sqrt{−{x}^{\mathrm{2}} }}\:\mathrm{is}\:\mathrm{not}\:\mathrm{defined}\:\forall{x}\in\mathbb{R} \\ $$