2025 IGCSE Additional Mathematics October/November 0606/23 Q2

8 marks

1. The diagram shows the graph of \(y=\mathrm f(x)\).
  On the same diagram sketch the graph of \(y=\mathrm f^{-1}(x)\).[1]
2. Describe the relationship between the graph of \(\mathrm f(x)\) and the graph of \(\mathrm f^{-1}(x)\).[1]
A function \(\mathrm g\) is defined by \(\mathrm g(x)=\mathrm e^{\sqrt{x-2}}\) for \(x\ge2\).
1. Find an expression for \(\mathrm g^{-1}(x)\).[3]
2. Write down the range of \(\mathrm g^{-1}\).[1]
3. A function \(\mathrm h\) is defined by \(\mathrm h(x)=\dfrac1{x^2}+2\) for \(x>0\).
  Find an expression for \(\mathrm{gh}(x)\) in its simplest form.[2]

Similar questions are unavailable for this question.

Answer:(a) Inverse sketch shown; reflection in \(y=x\). (b)(i) \((\ln x)^2+2\) (ii) \([2,\infty)\) (iii) \(\mathrm e^{1/x}\)

Need help? Join our JC Math tuition classes.