Given a computable function $f\colon D \rightarrow D$, can I make the following operations and still end up with a computable function? Or in other words: are the following operations computable?
- Scaling, i.e. for a rational number $r$, is $r\cdot f$ still computable? Multiplication here is meant in a pointwise matter.
- Taking the minimum/maximum between $f_1$ and $f_2$ (again pointwise)
- Additivity, i.e. is $f_1 + f_2$ (pointwise addition) computable?
I am fairly certain that these claims are true, but am not sure how to show it. Any help is appreciated!