2021 NJC Promo Q5 It is given that $text{f}left( x right)=left{ begin{matrix}{{left( x-2 right)}^{2}},0le x<2 \2x-4,2le xle 4 \end{matrix} right.$ and that $text{f}left( x right)=text{f}left( x+4 right)$ for all real
2021 ACJC Promo Q7 The functions $text{f}$ and $text{g}$ are defined by $text{f}:xmapsto frac{1}{left| 1-{{x}^{2}} right|}$, $xin mathbb{R}$, $-2le x<-1$,$text{g}:xmapsto -{{left( x-2 right)}^{2}}+k$, $xin mathbb{R}$, $xge 0$ where $k$ is
2021 NYJC Promo Q4 The function $text{f}$ is defined by $text{f}left( x right)=frac{1}{{{x}^{2}}+1}$, $xin mathbb{R}$, $xge k$. (i) State the minimum value of $k$ for which the function ${{text{f}}^{-1}}$ exists.
2022 YIJC Promo Q9 The function $text{f}$ is defined by $text{f}:xmapsto {{x}^{2}}-4x-5$, for $xin mathbb{R}$, $xle 2$. (a) Find ${{text{f}}^{-1}}left( x right)$ and state the domain of ${{text{f}}^{-1}}$. [3] (b)
2022 HCI P1 Q6 The function $text{f}$ is defined by $text{f}:xmapsto left{ begin{matrix}5+ln x,,,,,,,text{for},,0<x<1, \-{{x}^{2}}+6x,,,,text{for }1le xle a, \end{matrix} right.$ where $a$ is a constant. (i) Given that $text{f}$ has
2022 ACJC P1 Q6 The function $text{h}$ is defined by $text{h}:xmapsto left| ln left( 2x right) right|+1$, $xin mathbb{R}$, $0<xle lambda $. (i) Find the maximum value of $lambda $
2022 EJC P1 Q4 (a) The function $text{f}$ is defined by $text{f}:xmapsto {{left( x+3 right)}^{2}}-1$ for $xin mathbb{R}$, $xge -3$.Find ${{text{f}}^{-1}}left( x right)$, stating the domain of ${{text{f}}^{-1}}$. [3] (b)
2022 ACJC P2 Q1 The function $text{f}$ is defined by $text{f}left( x right)=1-ax$, $xin mathbb{R}$, where $a$ is a real constant. The function $text{g}$ is defined by $text{g}left( x right)=left{
2022 ASRJC P1 Q8 (a) Functions $text{f}$ and $text{g}$ are defined by $text{f}:xto {{x}^{2}}$, $x<0$.$text{g}:xto frac{1}{x}$, $x>0$. (i) Explain why the composite function $text{gf}$ exists. [1] (ii) Find the exact
2022 RI P1 Q9 The functions $text{f}$, $text{g}$ and $text{h}$ are defined as follows: $text{f}:xmapsto {{x}^{3}}-1$, $xin mathbb{R}$,$text{g}:xmapsto {{text{e}}^{-3x}}$, $xin mathbb{R}$, $x<0$,$text{h}:xmapsto frac{x+1}{x-1}$, $xin mathbb{R}$, $xne 1$. (i) Define in