Functions

2022 EJC J1 MYE Q3 Functions $text{g}$ and $text{h}$ are defined as $text{g}:xmapsto 7{{text{e}}^{-x}}-text{e}$, $xin mathbb{R}$, $x>0$,$text{h}:xmapsto {{x}^{2}}+2x+5$, $xin mathbb{R}$, $xle -1$. (i) Determine if the composite function $text{hg}$ exists.

2022 CJC J1 MYE Q7 The function $text{f}$ is defined by $text{f}:xto {{left( frac{3}{x-2} right)}^{2}}$, $xin mathbb{R}$, $x>2$. (i) Show that ${{text{f}}^{-1}}$ exists and define it in similar form. [5]

ASRJC Functions Tutorial Q9 The function $text{f}$ is defined by $text{f}:xmapsto left| 3+x-2{{x}^{2}} right|$ for $xin mathbb{R}$, $xle k$. (i) Find the greatest value of $k$ such that $text{f}$ has

2018 MI Promo Q10 Functions $text{f}$ and $text{g}$ are defined by $text{f}:xmapsto frac{1}{x-2},$ $xin mathbb{R},$ $xne 2,$$text{g}:xmapsto {{x}^{2}}-4x$, $xin mathbb{R}.$ (i) Determine whether the composite functions ${{text{f}}^{2}}$, $text{fg}$ and $text{gf}$

2013 AJC P2 Q1 The function $text{f}$ is defined by $text{f: }xmapsto frac{4}{{{left( 2x-5 right)}^{2}}+1}text{ for }xin mathbb{R},xle frac{5}{2}$. (i) Sketch the graph of $y=text{f}left( x right)$ and show that

2015 PJC P2 Q1 The function $text{f}$ is defined by $text{f}:xmapsto lambda x-{{x}^{2}},quad xin mathbb{R},quad x>frac{lambda }{2},$ where $lambda >2$. (i) Find, in terms of $lambda $, ${{text{f}}^{-1}}left( x right)$, stating

2022 ASRJC 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 the

2021 TMJC Promo Q5 Given that $a>0$, functions $text{f}$ and $text{g}$ are defined by $text{f}:xmapsto x+2+frac{4}{x-1}$ for $xin mathbb{R}$, $xne 1$,$text{g}:xmapsto ln left( x+a right)$ for $xin mathbb{R}$, $x>0$. (i)