DP Further Mathematics HL Questionbank

• Syllabus

4.3

Sub sections and their related questions

Functions: injections; surjections; bijections.

• 12M.2.hl.TZ0.4A.a: Show that \(f\) is a bijection if \(\boldsymbol{A}\) is non-singular.
• 12M.2.hl.TZ0.4A.b: Suppose now that \(\boldsymbol{A}\) is singular.   (i)     Write down the relationship between...
• 14M.1.hl.TZ0.13: The function...
• 15M.1.hl.TZ0.11: Prove that the function \(f:\mathbb{Z} \times \mathbb{Z} \to \mathbb{Z} \times \mathbb{Z}\)...
• 16M.1.hl.TZ0.1b: (i)     State the value of \(f(1)\), giving a reason for your answer. (ii)     Find...
• 16M.1.hl.TZ0.1c: Determine whether or not \(f\) is (i)     injective; (ii)    surjective.
• 18M.1.hl.TZ0.9a: Given that A is the interval \(\left\{ {x\,{\text{:}}\,0 \leqslant x \leqslant 3} \right\}\) and...
• 18M.1.hl.TZ0.9b.i: Show that the function \(f\) is a bijection.
• 18M.1.hl.TZ0.9b.ii: Hence find the inverse function \({f^{ - 1}}\).

Composition of functions and inverse functions.

• 18M.1.hl.TZ0.9a: Given that A is the interval \(\left\{ {x\,{\text{:}}\,0 \leqslant x \leqslant 3} \right\}\) and...
• 18M.1.hl.TZ0.9b.i: Show that the function \(f\) is a bijection.
• 18M.1.hl.TZ0.9b.ii: Hence find the inverse function \({f^{ - 1}}\).