Explicație pas cu pas:
a)
[tex]E(x) = ( \frac{1}{x + 2} - \frac{1}{2x + 1}) \div \frac{1}{2 {x}^{2} + 5x + 2} = \\ = \frac{2x + 1 - (x + 2)}{(x + 2)(2x + 1)} \div \frac{1}{(2x + 2)(x + 2)} \\ = \frac{2x + 1 - x - 2}{(2x + 2)(x + 2)} \times (2x + 2)(x + 2) \\ = x - 1[/tex]
b)
[tex]E(-x) = ( - x) - 1 = - (x + 1)[/tex]
[tex]E(-x) \times E(x) = - (x + 1)(x - 1) = - ( {x}^{2} - 1) = 1 - {x}^{2} [/tex]
[tex] {x}^{2} \geqslant 0 < = > - {x}^{2} \leqslant 0 = > 1 - {x}^{2} \leqslant 1 [/tex]
[tex] = > E(-x) \times E(x) \leqslant 1[/tex]
