2013 HCI C2 BT2 P1 Q11 [Modified] The functions $text{f}$, $text{g}$, $text{h}$ and $text{k}$ are defined by $text{f}:x,mapsto ,{{text{e}}^{-x}}-frac{1}{5}$, $xin mathbb{R}$; $text{g}:x,mapsto ,sqrt{text{f}left( x right)}$, $xin mathbb{R}$, $xle frac{3}{2}$; $text{h}:x,mapsto
2016 HCI P1 Q11 The functions $text{f}$ and $text{g}$ are defined by $text{f}:xmapsto frac{1}{2}{{e}^{1-{{x}^{2}}}},text{ }xin mathbb{R},text{ }xle 1$$text{g}:xmapsto sqrt{1-ln x},text{ }xin mathbb{R},text{ }0<xle e$. (i) Show that $text{gf}$ exists, and
2016 JJC Promo Q7 The functions $text{f}$ and $text{g}$ are defined by $begin{matrix}& text{f}:xmapsto left| x-2 right|,xin mathbb{R} \ & text{g}:xmapsto {{x}^{2}}-x,xin mathbb{R},xle 0 \ end{matrix}$ (i) By considering the
2015 IJC P1 Q6 The function $text{f}$ is defined by $text{f : }xmapsto {{text{e}}^{x-2}}-3, text{ }xin mathbb{R}$. (i) Find ${{text{f}}^{-1}}(x)$ and write down the domain and range of ${{text{f}}^{-1}}$. [3]
Functions Revision Set Tutorial Q2 The functions $text{f}$ and $text{g}$ are defined as follows: $begin{matrix}& text{f}:xmapsto {{x}^{3}}+1,xin mathbb{R}, \ & text{g}:xmapsto {{e}^{-2x}},xin mathbb{R} \ end{matrix}$ (i) Define in a similar
Functions Revision Set Tutorial Q1 The function $text{f}$ is given by $text{f}:xmapsto {{x}^{2}}-6lambda x,xin mathbb{R},$ where $lambda $ is a positive constant. Find, in terms of $lambda $, (i) $text{ff}left(
2008 HCI P1 Q8 The functions $text{f}$ and $text{g}$ are defined by $begin{matrix}& text{f}:xmapsto -{{e}^{left| 3-x right|}},xin mathbb{R}, \ & text{g}:xmapsto a-{{(x-1)}^{2}},xin mathbb{R}text{ and }atext{ is a constant} \ end{matrix}$
2008 AJC P1 Q11 The function $text{f}$ is defined by $text{f}:xto ln left[ {{left( x-1 right)}^{2}}-k right]$, where $x<-2$ and $k$ is a constant. Find the maximum value of $k$.
2009 TJC P1 Q8 The functions $text{f}$ and $text{g}$ are defined by $begin{matrix}& text{f}:xmapsto -{{(x-2)}^{2}}+4,xin mathbb{R},xle 2, \ & text{g}:xmapsto frac{1}{{{(x-7)}^{2}}-4},xin mathbb{R},xle k,xne 5,xne 9 \ end{matrix}$ (a) (i) Sketch
2013 NYJC P2 Q2 (a) The function $text{f}$ is defined by $text{f}:xmapsto frac{2x-1}{2x-2},quad x<1$. Define ${{text{f}}^{-1}}$ in a similar form. Hence or otherwise find ${{text{f}}^{2}}(x)$ and state the value of