If and
are two relations on
to
, then they are called equal if they are equal as subsets of
.
When applied to functions, this means are equal
if
i.e.,
, for each
.
& codomain of
codomain of
.
Some operations in functions:
Let then
(I) The addition of two functions,i.e., defined by
(ii) The multiplication is defined by
(iii) The quotient is defined by
where
(iv) The subtraction of the two functions,
Example:
(i)
(ii)
(iii)
(iv)
is not defined
.