Comment on Activity 2

There is only one additive function in this group. Functions (ii) - (vi) are not additive. For example, in (iii) we calculate `ftext[(]1+1text[)]=ftext[(]2text[)]=2^2=4`, but `ftext[(]1text[)]+ftext[(]1text[)]=1+1=2 text(.)` Similarly, in (v) we find `ftext[(]9+16text[)]=ftext[(]25text[)]=5`, but `ftext[(]9text[)]+ftext[(]16text[)]=3+4=7text(.)`

On the other hand, the function in (i) is additive. This function is a member of the class of functions with descriptions of the form `ftext[(]xtext[)]=c x`, and any function in this class is additive. To see this, we calculate

`ftext[(]a+btext[)]=ctext[(]a+btext[)]=ca+cb=ftext[(]atext[)]+ftext[(]btext[)]`.

As you have seen, additive functions are rather rare.