2013 DHS P1 Q2

2013 DHS P1 Q2

5 marks

Prelims

Without the use of a calculator, solve the inequality \(\frac{1}{x}+1\le x\left( 1+x \right)\).[3]

Hence, solve \(1-{{\mathrm{e}}^{2x}}+{{\mathrm{e}}^{-x}}-{{\mathrm{e}}^{x}}\le 0\).[2]

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Answer:(i) \(x<0\) or \(x\ge1\). (ii) \(x\ge0\).

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