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Beyond Horizon Set 2 Paper 2 · Q10

Paper 2Algebra

If xx is a real number and y=12(ex−e−x)y=\frac12(e^x-e^{-x}), then

Axx can be either log⁡(y+y2+1)\log(y+\sqrt{y^2+1}) or log⁡(y−y2+1)\log(y-\sqrt{y^2+1})
Bxx can only be log⁡(y+y2+1)\log(y+\sqrt{y^2+1})
Cxx can be either log⁡(y+y2−1)\log(y+\sqrt{y^2-1}) or log⁡(y−y2−1)\log(y-\sqrt{y^2-1})
Dxx can only be log⁡(y+y2−1)\log(y+\sqrt{y^2-1})

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