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Let $f=\left\{\left(x, \frac{x^2}{1+x^2}\right): x \in R\right\}$ be a function from $R$ into $R$. Determine the range of $f$.
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Let $y=f(x)=\frac{x^2}{1+x^2} ; f(x)$ is positive for all values of $x$ when $x=0, y=0$. Also denominator $>$ numerator
$\therefore$ Range of $f=\{y: y \in R$ and $y \in[0,1)\}$
$\therefore$ Range of $f=\{y: y \in R$ and $y \in[0,1)\}$
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