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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}
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1 Answer

  • 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 meena.p
edited Mar 27, 2013 by meena.p

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