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# Let $f\;:\;R\rightarrow R$ be defined by $f(x)\;=\;\frac{1}{x}\quad x\;\in\; R.$Then f is

\begin{array}{1 1}(A)\;one-one & (B)\;onto \\(C)\;bijective & (D)\; f \;is\; not\; defined\end{array}
Can you answer this question?

## 1 Answer

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Toolbox:
• 1.A function $f:R \to R$ is one-one if $f(x)=f(y)=>x=y \qquad x,y \in R$
• 2. A function $f:R \to R$ is onto if for every $y \in R$ then exists $x \in R$ such that $f(x)=y$
• 3.A function $f:R \to R$ is bijective if it is both one-one and onto
• 4.A function is defined in $f:R \to R$ if f(x) is true for all values of $x \in B$
Given $f: R \to R4 \qquad ; f(x)=\frac{1}{x} \qquad x \in R$

Let $x=0$

$f(x)=\frac{1}{0}$ is not defined

Solution: 'D' option is correct .

answered Mar 5, 2013 by
edited Mar 27, 2013 by meena.p

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