Writing the domain of a function (some points to consider).

In summary, when finding the domain of a function in Rn, we need to consider the expressions within the function and write appropriate restrictions. These can include writing x≥0 for √x, x≠0 for 1/x, x>0 for 1/√x, and x>0 for log(x). Additional points to consider could include 1/√(1/(x-3)2 - 1/(x-2)2) and arcsin x, 1 ≤ x ≤ 1.
  • #1
gikiian
98
0
For finding domain of a function in Rn, I have jot down some of the points. Assuming, if one or more of these 'x'es are a part of the expression of a function f(x1, x2, x3,…, xn), we do the following in writing down the domain:

- for √x we write x≥0
- for 1/x we write x≠0
- for 1/√x we write x>0
- for log(x) we write x>0

What can be some more points similar to the ones I wrote above?
 
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  • #2
welcome to pf!

hi gikiian! welcome to pf! :wink:

yes that's right :smile:
gikiian said:
What can be some more points similar to the ones I wrote above?

:rolleyes: … how about 1/√(1/(x-3)2 - 1/(x-2)2) ? :wink:
 
  • #3
arcsin x, 1 ≤ x ≤ 1 etc?
 

Related to Writing the domain of a function (some points to consider).

1. What is the domain of a function?

The domain of a function is the set of all possible input values for the function. It is the set of numbers or values that the function can accept as input.

2. How do you write the domain of a function?

To write the domain of a function, you need to consider the type of function and any restrictions or limitations on the input values. For example, for a linear function, the domain would be all real numbers. But for a rational function, you would need to consider any restrictions on the denominator, such as a value that would make it equal to zero.

3. What are some common restrictions on the domain of a function?

Some common restrictions on the domain of a function include excluding values that would result in division by zero, values that would result in taking the square root of a negative number, or values that would be undefined for the function.

4. Can the domain of a function change?

Yes, the domain of a function can change depending on the type of function and any restrictions on the input values. Also, if the function is composed of multiple functions, the domain may be limited by the domains of each individual function.

5. Why is it important to consider the domain of a function?

The domain of a function is important because it determines the set of values for which the function is defined and can provide insight into the behavior of the function. It also ensures that the function is well-defined and avoids any errors or undefined results. Additionally, knowing the domain can help with finding the range and solving equations involving the function.

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