Inverse of a restricted quadratic function and the range of a related square-root function
Inverse of a restricted quadratic function and the range of a related square-root function
6 marks
A function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=x^2-2x+6\) for \(x\leq1\).
- Find an expression for \(\mathrm{f}^{-1}(x)\) and write down the domain of \(\mathrm{f}^{-1}\).[4]
- The function \(\mathrm{g}\) is defined by \(\mathrm{g}(x)=3+\sqrt{\mathrm{f}(x)}\) for \(x\leq1\). Determine the range of \(\mathrm{g}\).[2]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
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 a free account to practise similar questions.
Answer:\(\mathrm f^{-1}(x)=1-\sqrt{x-5}\), domain \([5,\infty)\); range of \(\mathrm g\) is \([3+\sqrt5,\infty)\).
Need help? Join our JC Math tuition classes.
Learn more