Zeigen Sie: fa(-x)=-f-a(x)

Question

gegeben: $$ \frac { x+a }{ { x }^{ 2 } } $$       a∈ℝ\(o)

 

Zeigen Sie: f_a(-x)=-f_-a(x)

Answer 1

 

(x + a)/x²

 

f_a(-x) = (a - x)/(-x)² = (a - x)/x²

 

f_-a(x) = (x - a)/x² , also

-f_-a(x) = - (x - a)/x² = (a - x)/x² = f_a(-x)

 

Besten Gruß

Answer 2

Hi,

$$f_a(-x) = \frac{-x+a}{(-x)^2} = \frac{-x+a}{x^2} = -\frac{x-a}{x^2} = -f_{-a}(x)$$


Grüße