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| 1 | ( 2014 ) Let $N$ be the set of natural numbers. A function $f$ from $N$ to $N$ is given by, $f(x)=$ the sum of all factors of $x$. If $f(16)=8 p-9$, then find $f\left(p^{2}\right).$ $\qquad\mbox{ (3 marks)}$
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| 2 | ( 2012 ) A function $f$ is defined by $f: x \mapsto \frac{x+4}{2 x-1}, x \neq \frac{1}{2}$. Find the value of $p$ if $f\left(\frac{1}{p}\right)=p$. (3 marks)
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| 3 | ( 2013 ) A function $f$ from $A$ to $A$, where $A$ is the set of positive integers, is given by $f(x)=$ the sum of all positive divisors of $x$. Find the value of $k$, if $f(15)=3 k+6$. (3 marks)
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| 4 | ( 2011 ) Let the function $f: R \rightarrow R$ be given by $f(x)=c x+d$, where $c$ and $d$ are fixed real numbers. If $f(0)=-3$ and $f(2)=1$, find $c$ and $d$, and then find $f(9)$. (3 marks)
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| 5 | ( 2012 ) Let $f: R \rightarrow R$ be given by $f(x) =\frac{x+a}{x-2}, x \neq 2, f(8)=3$. Find the value of $a$ and $f^{-1}(7)$. (3 marks)
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| 6 | ( 2012 ) A function $f$ is defined by $f(x)=3 x-5$. Find the formula of $f^{-1}$. Find also the value of $k$, such that $f(k)=f^{-1}(k)$. (3 marks)
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| 7 | ( 2014 ) A function $f$ is defined by $f: x \mapsto \frac{3-x}{2 x}, x \neq 0$. Find the value of $x$ for which $f(x)=f^{-1}(x).$ $\qquad\mbox{ (3 marks)}$
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| 8 | ( 2014 ) The function $f$ is given by $f(x)=\frac{4 x-9}{x-2}, x \neq 2$. Find the value of $x$ for which $4 f^{-1}(x)=x.$ $\qquad\mbox{ (3 marks)}$
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| 9 | ( (2016/Myanmar/q02) ) The function $f$ is defined, for $x \in R$, by $f(x)=2 x-3$. Find the value of $x$ for which $f(x)=f^{-1}(x)$. (3 marks)
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| 10 | ( 2010 ) Given that $f(x)=\frac{x+a}{x-3}, x \neq 3$, and $f(8)=3$, find the value of $a$ and $f^{-1}(11)$.$\text{ (3 marks)}$
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| 11 | ( 2011 ) Let $f: R \rightarrow R$ be given by $f(x)=\frac{4 x+5}{a x-1}, x \neq \frac{1}{a}, f^{-1}(3)=1$, find $a$. (3 marks)
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| 12 | ( 2012 ) A function $f$ is defined by $f(x)=\frac{x}{a}+a$. If $f^{-1}(3)=2$, find the values of $a$. (3 marks)
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| 13 | ( 2012 ) A function $f$ is such that $f(x)=\frac{2}{k x+3}$ for all $x \neq-\frac{3}{k}$ where $k \neq 0$. If $f(-1)=2$, find the value of $k$ and the formula of $f^{-1}$. (3 marks)
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| 14 | ( 2010 ) A function $f: R \rightarrow R$ is defined by $f(x)=\frac{a x-9}{x-1}, x \neq 1$.If $f^{-1}(-1)=6$, find the value of $a$ and evaluate the image of 3 under $f$.$\text{ (3 marks)}$
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| 15 | ( 2010 ) A function $f$ is defined by $f(x)=\frac{5 x+3}{x-4}$ where $x \neq 4$.Find the formula of $f^{-1}$.$\text{ (3 marks)}$
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| 16 | ( 2014 ) Let $f(x)=\frac{3 x}{x-4}, x \neq 4$. Find the formula of $f^{-1}$. $\qquad\mbox{ (3 marks)}$
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| 17 | ( 2014 ) Find the formula for $f^{-1}$, the inverse function of $f$ defined by $f(x)=\frac{2}{3-4 x}$. State the suitable domain of $f.$ $\qquad\mbox{ (3 marks)}$
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| 18 | ( 2014 ) Let the mapping $\odot$ be defined by $(x, y) \rightarrow x \odot y=x+2 y$, where $x$ and $y$ are in $A=\{0,1,2\}.$ Is this mapping a binary operation? $\qquad\mbox{ (3 marks)}$
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| 1 | $31 \quad$
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| 2 | $p=-1$
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| 3 | $k=6$
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| 4 | $c=2, d=-3, f(9)=15$
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| 5 | $a=10 ; f^{-1}(7)=4$
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| 6 | $f^{-1}(x)=\frac{x+5}{3};k=\frac{5}{2}$
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| 7 | $x=-\frac{3}{2}$ (or) $x=1 \quad$
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| 8 | $x=6$
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| 9 | $x=3$
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| 10 | 7;4
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| 11 | $a=4$
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| 12 | $a=1$ (or) $a=2$
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| 13 | $k=2 ; f^{-1}(x)=\frac{2-3 x}{2 x}, x \neq 0$
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| 14 | $\frac{2}{3} ;-\frac{7}{2}$
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| 15 | $\frac{4 x+3}{x-5}, x \neq 5$
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| 16 | $f^{-1}(x)=\frac{4 x}{x-3}, x \neq 3$
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| 17 | $f^{-1}(x)=\frac{3 x-2}{4 x}, x \neq 0,\left\{x \mid x \in R, x \neq \frac{3}{4}\right\} \quad$
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| 18 | The closure property is not satified, $\odot$ is not a binary operation.
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