Domain of f(x) = (2x^2 + 25)^(0.5) + 1 - Help Needed

  • Context: High School 
  • Thread starter Thread starter garyljc
  • Start date Start date
  • Tags Tags
    Domain Function
Click For Summary

Discussion Overview

The discussion revolves around determining the domain of the function f(x) = (2x^2 + 25)^(0.5) + 1. Participants explore the appropriate notation for expressing the domain and clarify the distinction between the domain and the range of the function.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about the symbol to denote the domain of the function, suggesting that f(x) will always be greater than or equal to zero.
  • Another participant asserts that the domain is all real numbers, denoted as x ∈ ℝ, and specifies that the codomain is all real numbers greater than or equal to 6.
  • A participant confirms that ℝ denotes real numbers and questions whether the integers, denoted as ℤ, could also represent the domain.
  • It is noted that while integers are part of the domain, the full domain is ℝ, as the function accepts all real inputs, including non-integer values.
  • One participant comments on the nature of domain questions, suggesting that the domain is inherent in the function's definition and not something to be "found."
  • Another participant emphasizes that the function's value being always non-negative does not determine the domain; rather, it is the positivity of the expression under the square root that ensures the domain is ℝ.
  • A later reply mentions that the notation D(f) is typically used to denote the domain of a function.

Areas of Agreement / Disagreement

Participants generally agree that the domain of the function is all real numbers, but there is some discussion about the relevance of integers as a subset of the domain. The distinction between domain and range is also highlighted, indicating some level of conceptual clarification is needed.

Contextual Notes

There is a lack of consensus on the implications of the domain being defined as all real numbers versus integers, and the discussion includes various interpretations of how to express the domain symbolically.

Who May Find This Useful

Readers interested in function analysis, mathematical notation, and the concepts of domain and range in mathematics may find this discussion relevant.

garyljc
Messages
103
Reaction score
0
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
 
Mathematics news on Phys.org
The domain is all values of x, so you can say the domain is all real numbers, or [tex]x\in \Re[/tex]. The Codomain is all real numbers greater or equal to 6, or the set [tex][6, \infty)[/tex]
 
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.
 
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.
 
garyljc said:
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.

garyljc said:
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 "[itex]f(x)= \sqrt{2x^2+ 25}+ 1[/itex] with domain all integers" is a very different function from "[itex]f(x)= \sqrt{2x^2+ 25}+ 1[/itex] with domain all real numbers".
 
garyljc said:
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 =)
 

Similar threads

High School Domain of a composite function
  • · Replies 11 ·
Replies
11
Views
2K
MHB What are the domain and range for the inverse function $f^{-1}$ of $f$?
  • · Replies 2 ·
Replies
2
Views
2K
High School Can Negative Numbers Be in the Domain of the Square Root Function?
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Domain of the identity function after inverse composition
  • · Replies 3 ·
Replies
3
Views
2K
MHB Math Notation: How to explicitly specify the domain of a function symbolically?
  • · Replies 11 ·
Replies
11
Views
12K
MHB GRE.al.4 Find the domain of \sqrt{x^2-25}
  • · Replies 3 ·
Replies
3
Views
1K
High School Inverse Functions vs Inverse Relations
  • · Replies 4 ·
Replies
4
Views
4K
MHB Find the domain and range of the following function f(x)=x-2/sqrt(10-2x)
  • · Replies 2 ·
Replies
2
Views
3K
MHB Finding Domain of f(x)=\frac{1}{x^{2}-x-6}
  • · Replies 5 ·
Replies
5
Views
3K
MHB Finding Domain & Range of $$y=\sqrt{x^2+y^2}$$
  • · Replies 8 ·
Replies
8
Views
3K