QUESTION 04 Functions \(f\) and \(g\) are defined as follows: \(f : x \rightarrow x^{2}+2x+3\) for \(x \le -1\)...

QUESTION 20 In the diagram, the graph of \(y=f(x)\) is shown with solid lines. The graph shown with broken...

QUESTION 05 The functions \(f\) and \(g\) are defined by: \(f(x)=x^{2}-4x+3\) for \(x > c\), where \(c\) is a...

QUESTION 06 The function \(f\) is defined by \(f : x \rightarrow 7-2x^{2}-12x\) for \(x \in \mathbb{R}\). (i) Express...

QUESTION 07 (i) Express \(9x^{2}-6x+6\) in the form \((ax+b)^{2}+c\), where \(a\), \(b\) and \(c\) are constants.   The...

QUESTION 08 Functions \(f\) and \(g\) are defined by: \(f : x \rightarrow \dfrac{3}{2x+1}\) for \(x > 0\) \(g...

QUESTION 09 The function \(f\) is defined by \(f(x)=3x+1\) for \(x \le a\), where \(a\) is a constant. The...

QUESTION 10 (a) Express \(2x^{2}+12x+11\) in the form \(2(x+a)^{2}+b\), where \(a\) and \(b\) are constants.   The one-one...

QUESTION 11 The function \(f\) is defined by \(f(x)=\dfrac{48}{x-1}\) for \(3\le x\le7\). The function \(g\) is defined by \(g(x)=2x-4\)...

QUESTION 12 The diagram below shows the graph of \(y=f(x)\). (a) On this diagram, sketch the graph of \(y=f^{-1}(x)\)....