Tim Gan Math
Sign up free

2020 IGCSE Additional Mathematics May/June 0606/12 Q5

2020 IGCSE Additional Mathematics May/June 0606/12 Q5

9 marks

\(\mathrm{f}:x\mapsto(2x+3)^2\quad\text{for}\hspace{0.5em}x>0\)

  1. Find the range of \(\mathrm{f}\).[1]
  2. Explain why \(\mathrm{f}\) has an inverse.[1]
  3. Find \(\mathrm{f}^{-1}\).[3]
  4. State the domain of \(\mathrm{f}^{-1}\).[1]
  5. Given that \(\mathrm{g}:x\mapsto\ln(x+4)\) for \(x>0\), find the exact solution of \(\mathrm{fg}(x)=49\).[3]

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create free accountSign inMath tuition

Create a free account to practise similar questions.

Create free accountSign inMath tuition
Answer:(a) \(\mathrm{f}(x)>9\) (b) \(\mathrm{f}\) is one-one on the restricted domain \(x>0\) (c) \(\mathrm{f}^{-1}:x\mapsto\dfrac{\sqrt{x}-3}{2}\) (d) \(x>9\) (e) \(x=\mathrm{e}^2-4\)

Need help? Join our JC Math tuition classes.

Learn more