In this list, the functions described in (i), (ii), (iv), and (vi) are not multiplicative. For example, for (i) we find `ftext[(]1 cdot 1text[)]=ftext[(]1text[)]=-2`, but `ftext[(]1text[)]cdotftext[(]1text[)]=text[(]-2text[)]cdottext[(]-2text[)]=4`. For (vi) we calculate `ftext[(]1 cdot 2text[)]=ftext[(]2text[)]=text(log) 2`, but `ftext[(]1text[)]cdotftext[(]2text[)]=0 cdot text(log) 2=0 text(.)`
On the other hand, the square and square root functions are both multiplicative. In fact, any power function `f` with a description of the form
`ftext[(]xtext[)]=x^k`
is multiplicative. To see this, we calculate
`ftext[(]a cdot btext[)]=text[(]a cdot btext[)]^k=a^k b^k=ftext[(]atext[)]cdotftext[(]btext[)]`.
Again, multiplicative functions would seem to be rather rare.