2016 ACJC P2 Q3 The functions $text{h}$ and $text{g}$ are defined by $text{h}:xmapsto {{e}^{left| 2x+1 right|}}+1,text{ }xin mathbb{R},text{ }xle k$$text{g}:xmapsto $ $left{ begin{matrix}2xtext{ for }0le xle frac{1}{2} \2-2xtext{ for }frac{1}{2}le
2016 PJC P2 Q3 The function $text{f}$ is defined by $text{f}(x)=left{ begin{matrix}& frac{x}{2}text{ if }xle 0 \ & 2sin xtext{ if }0<xle 4 \ end{matrix} right.$ (i) Sketch the graph
2015 VJC P1 Q4 The function $text{g}$ is defined by $text{g}:xmapsto {{e}^{x}}-7x,x>lambda $, where $lambda $ is a real constant. (i) Find the exact minimum value of $lambda $ such
2019 NJC P2 Q1 It is given that $text{f}left( x right)=left{ begin{matrix}& ax,text{for }0le x<2, \ & frac{12a}{x}-4a,text{for }2le x<3, \ end{matrix} right.$ where $a$ is a positive constant and
2022 ASRJC J2 MYCT P1 Q8 The function $text{f}$ is defined by $text{f}:xmapsto 1+ax-{{x}^{2}}$, $xin mathbb{R}$, $xle k$ where $a$ is a positive constant. (i) Explain with a sketch why
2021 ACJC P1 Q3 The function $text{f}$ is defined as $text{f}:xmapsto frac{a}{2-x}$, $xin mathbb{R}$, $xne 0,2$. (i) Find ${{text{f}}^{2}}$ and ${{text{f}}^{-1}}$ in terms of $a$, stating their domains clearly. [5]
2022 TJC J2 MYE P1 Q2 By expressing $sin 3x-cos 3x$ in the form $Rsin left( 3x-alpha right)$, where $R>0$ and $0<alpha <frac{pi }{2}$, describe a sequence of transformations that
2022 CJC J1 MYE Q8 The functions $text{g}$ and $text{h}$ are defined as $text{g}:xto left{ begin{matrix} 4{{left( x+1 right)}^{2}}text{ for }xin mathbb{R}text{, }-3le x<0, \ 4x+4text{
2022 VJC J1 MYE Q3 It is given that $text{f}left( x right)=left{ begin{matrix}left| x right|text{ for -1}<xle 2, \1text{ for 2}<xle 4, \end{matrix} right.$ and that $text{f}left( x+5 right)=text{f}left( x
2017 NJC Promo Q7 The functions $text{f}$ and $text{g}$ are defined as $text{f}:xmapsto frac{3x}{2x-5},$ for $-5<xle 5$, $xne frac{5}{2}$ $text{g}left( x right)=left{ begin{matrix}8x-{{x}^{2}}-15,text{ for }3le x<4. \frac{5-x}{2},text{ for }4le x<6.