Math Help Forum: Codomain of a function

Hello everybody,
i'm ashamed about this question but... Here it goes:

i have this function,

and i am suddenly requested to calculate its Codomain.. I got stuck..

I mean, i realized i have no real "method" to calculate the Codomain of a function, so, how should i go around this? There is a valid "method" to solve those kind of problems?

Thanks in advance,
SkyWolf.

Originally Posted by SkyWolf

Hello everybody,
i'm ashamed about this question but... Here it goes:

i have this function,

and i am suddenly requested to calculate its Codomain.. I got stuck..

I mean, i realized i have no real "method" to calculate the Codomain of a function, so, how should i go around this? There is a valid "method" to solve those kind of problems?

Thanks in advance,
SkyWolf.

Why are you ashamed?

Note that the quantity under the square root sign is positive. So, the codomain is .

Originally Posted by alexmahone

Why are you ashamed?

Note that the quantity under the square root sign is positive. Furthermore, . (Just square both sides in order to prove this.)

So, the codomain is (the set of all positive real numbers).

Ashamed 'cause it should be somewhat "easy" to tell something basic like the codomain.

Anyways, thanks for the reply regarding this particular problem, but, should i assume that there is no real "method" to find the codomain? It is all deduction-based? (like, this is positive, so ...)

Thanks again,
SkyWolf.

Originally Posted by SkyWolf

Ashamed 'cause it should be somewhat "easy" to tell something basic like the codomain.

Anyways, thanks for the reply regarding this particular problem, but, should i assume that there is no real "method" to find the codomain? It is all deduction-based? (like, this is positive, so ...)

Thanks again,
SkyWolf.

Note that I edited my answer. is false. (Sorry about that!)

The codomain is a set within which the values of a function lie. So, is a codomain of every function. In this problem, I was able to find a smaller codomain by noting that the function always takes real values.

Note that a function can have several codomains. Both and are codomains of your function.

Originally Posted by SkyWolf

i have this function,

and i am suddenly requested to calculate its Codomain.

The function is .
Graph the function.
Do you see that is the maximum?
Is it true that

Can you find

Originally Posted by Plato

The function is .
Graph the function.
Do you see that is the maximum?
Is it true that

Can you find

I really don't think all this is necessary. Note that the OP is trying to find the codomain, not the range.

Originally Posted by alexmahone

I really don't think all this is necessary. Note that the OP is trying to find the codomain, not the range.

In most some usage the are synonymous.
Also see this.

Originally Posted by Plato

In most common usage are synonymous.
Also see this.

But WolframMathWorld says that they are not synonymous.