[SOLVED]How to understand Domain Convention

Casio

Member
I keep reading through the course text book but no matter how many times I read it I just can't see the understanding of it?

There are activities asking me to solve problems, and I have a book of exercises to do, but the main book supposed to be designed to give some information to the student to gain an insight into understanding is somewhat very poorly presented

What seems to be very confusing to me at the moment is the interpretation of the notation used.

example.

If y = x^2, then

x is the input, which is then processed to become x^2.

So y(x) = x^2 I think?

y is the function

x is the domian

x^2 is the rule

Have I got this right so far?

if

f(x) = x^2 + 1 (0 < x < 6)

I understand inequalities so this does not require explaining, but in this example the domain is (x), the rule is x^2 + 1, and the inequalities in brackets with real numbers are used in (x) are they?

f(0) = 0^2 + 1, or

f(6) = 6^2 + 1, or is it 0 < 6 in other words the domain can be any number between 0 to 6 used in the rule?

If somebody could please advise if I am understanding the above correctly or not would be much appreciated as I can't get this from my coursebook because there is no worked examples or explanations.

Thanks

Plato

Well-known member
MHB Math Helper
I keep reading through the course text book but no matter how many times I read it I just can't see the understanding of it?

There are activities asking me to solve problems, and I have a book of exercises to do, but the main book supposed to be designed to give some information to the student to gain an insight into understanding is somewhat very poorly presented

What seems to be very confusing to me at the moment is the interpretation of the notation used.

example.

If y = x^2, then

x is the input, which is then processed to become x^2.

So y(x) = x^2 I think?

y is the function

x is the domian

x^2 is the rule

Have I got this right so far?

if

f(x) = x^2 + 1 (0 < x < 6)

I understand inequalities so this does not require explaining, but in this example the domain is (x), the rule is x^2 + 1, and the inequalities in brackets with real numbers are used in (x) are they?

f(0) = 0^2 + 1, or

f(6) = 6^2 + 1, or is it 0 < 6 in other words the domain can be any number between 0 to 6 used in the rule?
I think if you would post a problem using its exact wording with the exact set of instructions, then we can help you work through it.

Casio

Member
Thank you but I do need to clarify some basic understanding of the notation of the subject first, although I appreciate I created a long thread previously I will try to shorten it.

Casio

Member
Now that I have had some basics explained to me on another thread entitled "Understanding Functions" I can now understand what the title of this thread now means.

By example;

g(x) = sqrt x

The function of g has the domain {0, infinity) since sqrt x is defined only for x > 0

The x which is a variable would only represent a positive number since we cannot take the square root of a negative number, therefore x must be 0 or more than and cannot be negative.

Now I understand where {0, infinity} comes into it because x cannot be less than 0, but could be any number above 0.

Do you all agree.

HallsofIvy

Well-known member
MHB Math Helper
I keep reading through the course text book but no matter how many times I read it I just can't see the understanding of it?

There are activities asking me to solve problems, and I have a book of exercises to do, but the main book supposed to be designed to give some information to the student to gain an insight into understanding is somewhat very poorly presented

What seems to be very confusing to me at the moment is the interpretation of the notation used.

example.

If y = x^2, then

x is the input, which is then processed to become x^2.

So y(x) = x^2 I think?

y is the function
Yes, that is correct.

x is the domian
No, x is the "variable". The general rule is that unless something specific is said (like "$0\le x\le 6$" later) the domain is all values of x for which the operations involved are defined. Here, the only operations are "square" and "add 1" which can be done for all numbers.

x^2 is the rule
Yes.

Have I got this right so far?

if

f(x) = x^2 + 1 (0 < x < 6)

I understand inequalities so this does not require explaining, but in this example the domain is (x), the rule is x^2 + 1, and the inequalities in brackets with real numbers are used in (x) are they?

f(0) = 0^2 + 1, or

f(6) = 6^2 + 1, or is it 0 < 6 in other words the domain can be any number between 0 to 6 used in the rule?

If somebody could please advise if I am understanding the above correctly or not would be much appreciated as I can't get this from my coursebook because there is no worked examples or explanations.

Thanks