\[\boxed{\text{20\ (20).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[y = \frac{x^{2}}{x^{2} + 1} = \frac{x^{2} + 1 - 1}{x^{2} + 1} =\]
\[= \frac{x^{2} + 1}{x^{2} + 1} - \frac{1}{x^{2} + 1} = 1 - \frac{1}{x^{2} + 1}.\]
\[x^{2} + 1 \geq 1\ при\ любом\ \]
\[значении\ x \Longrightarrow D(y) = R.\]
\[Так\ как\ \ \ x^{2} + 1 \geq 1:\]
\[0 < \frac{1}{x^{2} + 1} \leq 1\ \ \ \ \ | \cdot ( - 1)\]
\[0 > - \frac{1}{x^{2} + 1} \geq - 1\ \ \ \ \ \ | + 1\]
\[- 1 + 1 \leq - \frac{1}{x^{2} + 1} + 1 < 0 + 1\]
\[0 \leq 1 - \frac{1}{x^{2} + 1} < 1.\]
\[E(y) = \lbrack 0;1).\]