SAJC Functions Tutorial Q11
The functions $\text{f}$ and $\text{g}$ are defined as follows
$\text{f}:x\mapsto \sin x$, $x\in \mathbb{R}$, $-\pi \le x\le 2\pi $.
$\text{g}:x\mapsto \cos x$, $x\in \mathbb{R}$, $0\le x\le 2\pi $.
(i)
Sketch the graph of $y=\text{f}\left( x \right)$ and explain why ${{\text{f}}^{-1}}$ does not exist.
The function $\text{h}$ is a restriction on $\text{f}$ such that $\text{f}$ and $\text{h}$ share the same range, and both the functions ${{\text{h}}^{-1}}$ and $\text{g}{{\text{h}}^{-1}}$ exists.
(ii)
Write down the domain of $\text{h}$.
(iii)
Determine the range of $\text{g}{{\text{h}}^{-1}}$.
(iv)*
Find ${{\text{h}}^{-1}}$ in a similar form.
Suggested Video Solutions
Our H2 Math Tuition includes
- Question Bank with Video solutions to 1400+ questions
- Online Portal
- H2 Math Summary Notes
- Structured Curriculum and Notes
Share with your friends!
Continue reading
5 Exam Preparation Tips: How We Help Students Excel in Exams
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
List MF 27
What is the MF 27? The MF 27, set to replace the MF 26 from 2025, is a comprehensive formula sheet developed by the Ministry of Education Singapore in collaboration
Panic No More: What To Do The Day Before An Exam?
As you approach the final hours before your exam, remember that a balanced approach is key. A light review can keep the information fresh in your mind, while preparing your