Difference b/w range and codomain.
Can someone for the love of god explain to me the difference between range and codomain?
As per all the videos I’ve seen, codomain is defined as “Set of all possible outputs of a function”
For example:
f(x) = x^2
Literally impossible to have any negative number as an output with this function. Yet in all those videos they said:
“The codomain for x^2 will be set of all real numbers”
Should it not be set of all positive real numbers union with 0?
And agar aisa hi hai phir toh difference hua hi nahi codomain aur range mein? (pls help)
6 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.Okay, so the codomain is something that we define along with the function.
Jaise, we say consider a function f: ℝ→ℝ such that f(x) = sin(x) right?
In which case, the second R, the one after the arrow, is called the codomain. You can think of it as some set that we are choosing our outputs from. We are saying that this function sin(x) will always give a real number as an output, and never say, i (√-1)
However, the size of the output set need not be the entirety of the codomain.
That output set can be any subset of the codomain, and that is decided by the nature of the function. Whatever the function spits out as an output is considered part of the range. If it is possible for the function to output every single value in the codomain we chose, then, sure, the range is equal to the codomain. But, say we have a function, that, because of how we define it, cannot output a value that in the codomain. Then that isn't an issue. The value is still part of our choice of output values that we allow, but the function doesn't output it for any choice of input. So, that value would not be part of the range, but still part of the codomain.
so basically, codomain may contain more elements than the elements is the range, but range is always a subset of the codomain?
say for a function from A -> B
Codomain is all the elements of B
but Range CONTAINS elements of B
sometimes all sometimes none
Range is subset of Codomain
understood, understood
thanks for helping! @Gamertug