so i am having hard time understanding the idea of coming up with random n-vectors to disprove the superposition equality $f(\alpha x + \beta y) = \alpha f(x) + \beta f(y)$.
or to prove that a function is linear or affine???
can someone explain to me for the following function examples?
- $f(x) = \min x_i$
- $f(x) = \sum_{i=1}^n|x_i|$
- $f(x) = \sum_{i=1}^n|x_{i + 1} - x_i|$