clear
question: What kind of context makes it okay to drop the domain and codomain specification?, context: (with different domain) is not considered the same function, even though the formulas defining f and g agree, and similarly with a different codomain. Despite that, many authors drop the specification of the domain and codomain, especially if these are clear from the context. So in this example many just write f(x) = 4 − x. Sometimes, the maximal possible domain is also understood implicitly: a formula such as 




f
(
x
)
=



x

2


−
5
x
+
6





{\displaystyle \scriptstyle f(x)={\sqrt {x^{2}-5x+6}}}

 may mean that the domain of f is the set of real numbers x where the square root is defined (in this case x ≤ 2 or x ≥ 3).
What kind of context makes it okay to drop the domain and codomain specification?
Despite that, many authors drop the specification of the domain and codomain, especially if these are clear from the context.
(with different domain) is not considered the same function, even though the formulas defining f and g agree, and similarly with a different codomain. Despite that, many authors drop the specification of the domain and codomain, especially if these are clear from the context. So in this example many just write f(x) = 4 − x. Sometimes, the maximal possible domain is also understood implicitly: a formula such as 




f
(
x
)
=



x

2


−
5
x
+
6





{\displaystyle \scriptstyle f(x)={\sqrt {x^{2}-5x+6}}}

 may mean that the domain of f is the set of real numbers x where the square root is defined (in this case x ≤ 2 or x ≥ 3).
Despite that, many authors drop the specification of the domain and codomain, especially if these are <hl> clear <hl> from the context.
(with different domain) is not considered the same function, even though the formulas defining f and g agree, and similarly with a different codomain. Despite that, many authors drop the specification of the domain and codomain, especially if these are <hl> clear <hl> from the context. So in this example many just write f(x) = 4 − x. Sometimes, the maximal possible domain is also understood implicitly: a formula such as f ( x ) = x 2 − 5 x + 6 {\displaystyle \scriptstyle f(x)={\sqrt {x^{2}-5x+6}}} may mean that the domain of f is the set of real numbers x where the square root is defined (in this case x ≤ 2 or x ≥ 3).
(with different domain) is not considered the same function, even though the formulas defining f and g agree, and similarly with a different codomain. <hl> Despite that, many authors drop the specification of the domain and codomain, especially if these are clear from the context. <hl> So in this example many just write f(x) = 4 − x. Sometimes, the maximal possible domain is also understood implicitly: a formula such as f ( x ) = x 2 − 5 x + 6 {\displaystyle \scriptstyle f(x)={\sqrt {x^{2}-5x+6}}} may mean that the domain of f is the set of real numbers x where the square root is defined (in this case x ≤ 2 or x ≥ 3).