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2020 IGCSE Additional Mathematics October/November 0606/13 Q3

2020 IGCSE Additional Mathematics October/November 0606/13 Q3

7 marks
  1. \(\mathrm{f}(x)=4\ln(2x-1)\)
    1. Write down the largest possible domain for the function \(\mathrm{f}\).[1]
    2. Find \(\mathrm{f}^{-1}(x)\) and its domain.[3]
  2. \(\mathrm{g}(x)=x+5\quad\text{for}\hspace{0.5em}x\in\mathbb{R}\)
    \(\mathrm{h}(x)=\sqrt{2x-3}\quad\text{for}\hspace{0.5em}x\ge\dfrac32\)
    Solve \(\mathrm{gh}(x)=7\).[3]

Solution:

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Answer:(a)(i) \(x>\dfrac12\) (ii) \(\mathrm{f}^{-1}(x)=\dfrac12\left(1+\mathrm{e}^{\frac{x}{4}}\right)\), domain \(x\in\mathbb{R}\) (b) \(x=\dfrac72\)

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