Question

Докажите, что функция чётная

Answer 1

$f( - x) = \\ = 7cos ^{2} ( - 4x) + 3( - x) ^{2} = \\ = 7cos ^{2} ( 4x) + 3x ^{2} = f( x)$

$f( - x) = \frac{ {( - x)}^{2} - ( - x)}{ - x + 2} - \\ - \frac{ {( - x)}^{2} + ( - x) }{ - x - 2} = \\ = - \frac{ {x}^{2} + x }{x - 2} + \frac{ {x}^{2} - x}{x + 2} = \\ = \frac{ {x}^{2} - x}{x + 2} - \frac{ {x}^{2} + x }{x - 2} = f(x)$