2025 IGCSE Additional Mathematics October/November 0606/11 Q4

2025 IGCSE Additional Mathematics October/November 0606/11 Q4

10 marks
  1. Explain why this graph does not represent a function.[1]
  2. The table shows the graphs of four different functions.
    is one-oneis many-oneis its own inverse
    Tick (✓) each correct box in the table.
    There may be more than one tick in a row or a column.[4]
  3. Functions \(\mathrm f\) and \(\mathrm g\) are defined as follows.
    \(\mathrm f:x\mapsto\sin x\quad\text{for}\hspace{0.5em}30^\circ\le x\le a^\circ\)
    \(\mathrm g:x\mapsto\sqrt{x-\dfrac12}\quad\text{for}\hspace{0.5em}x\ge\dfrac12\)
    It is given that the function \(\mathrm{gf}\) exists.
    1. Find the value of \(a\) so that the domain of \(\mathrm{gf}\) is as large as possible.
      You may use the information that \(\sin30^\circ=\dfrac12\).[2]
    2. For the domain found in part (i), find the range of the function \(\mathrm{gf}\).[2]
    3. Determine whether the function \(\mathrm g^2\) exists.[1]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(a) Fails the vertical line test. (b) Rows 1 and 3: many-one; row 2: one-one and its own inverse; row 4: one-one. (c)(i) \(a=150\) (ii) \(0\le\mathrm{gf}(x)\le\dfrac1{\sqrt2}\) (iii) Does not exist.

Need help? Join our JC Math tuition classes.

Learn more