# Domain of a function

I was wondering if there's any symbol i could use for the domain of this question

f(x) = (2x^2 + 25)^(0.5) + 1

as we can see that , f(x) will always be greater or equal to zero , was wondering what would the domain be ? Could anyone help me out ? thanks

nicksauce
Homework Helper
The domain is all values of x, so you can say the domain is all real numbers, or $$x\in \Re$$. The Codomain is all real numbers greater or equal to 6, or the set $$[6, \infty)$$

oh that's the symbol i was thinking about R (which denotes real numbers right ?)
what about Z that denotes integers
is that a possible answer ?

Yes, R denotes the real numbers. The integers comprise part of the domain since x can be integers, however the full domain is R.

Maybe I can explain what the domain is for you. Think of the function like a machine. The domain is all of the possible inputs that you put in and the range is all of the possible answers that come out. Pretty simple.

So, can x's be something other than integers(1,2,3...)? what about .23614? Do you still get a valid answer? If so, (you do lol) then the integers are not all of the possible inputs. Hopefully that will help.

Gib Z
Homework Helper
Having much experience of the ineptly worded questions myself, I won't fret too much about it, but if someone like matt grime sees a "domain on this function.." type question, he may break something =]

That is because really, the domain is not meant to be "found", it is already part of the original functions definition. The function f(x) = x, 0 < x < 1, is a very different function to g(x)= x, 0< x < infinity.

HallsofIvy
Homework Helper
I was wondering if there's any symbol i could use for the domain of this question

f(x) = (2x^2 + 25)^(0.5) + 1

as we can see that , f(x) will always be greater or equal to zero , was wondering what would the domain be ? Could anyone help me out ? thanks
The fact that the function value "will always be greater or equal to zero" has nothing to do with the domain- it's the fact that the function value always exists that makes the domain R. And, since the only reason a function like this might not have a value would be that you can't take the square root of a negative number, that is due to the fact that 2x2+ 25 is always positive.

oh that's the symbol i was thinking about R (which denotes real numbers right ?)
what about Z that denotes integers
is that a possible answer ?
A possible answer to what question? Since the integers are a subset of all real numbers, certainly this function is defined for all integers. But the function "$f(x)= \sqrt{2x^2+ 25}+ 1$ with domain all integers" is a very different function from "$f(x)= \sqrt{2x^2+ 25}+ 1$ with domain all real numbers".

I was wondering if there's any symbol i could use for the domain of this question \
Typically it's denoted D(f)

thanks all for your help ... much appreciated ... now i understand more clearly thanks =)