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Question Number 13811 by Tinkutara last updated on 23/May/17

$$\mathrm{The}\mathrm{domain}\mathrm{of}f\left(x\right)=\sqrt{2-2^x-2^{2x}}\mathrm{is}?$$

Commented by RasheedSindhi last updated on 24/May/17

$$\mathrm{Sorry},\mathrm{wrong}\mathrm{process}.$$

Answered by ajfour last updated on 23/May/17

$$let{2}^x=t>0....\left(i\right)$$$$\Rightarrow t^2+t-2⩽0$$$$t^2+2t-t-2⩽0$$$$(t-1)(t+2)⩽0$$$$\Rightarrow -2⩽t⩽1....\left(ii\right)$$$$from\left(i\right)and\left(ii\right),$$$$0<t(=2^x)⩽1$$$$\Rightarrow x\in (-\mathrm{\infty },0].$$

Commented by Tinkutara last updated on 23/May/17

$$\mathrm{Thanks}.$$

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