i need to find the domain

L

logistic_guy

Full Member
Joined
Apr 17, 2024
Messages
287
this is the question

Find the domain of f(x) = (x^2 - x - 6) / x - 5. there is no tap to write the square root so i write brackets (x^2 - x - 6).

it is clear 5 is the domain of the function. it keeps telling me wrong. i know 5 - 5 = 0 this is invalid in the fraction when it is written down.

there is no tap for infinite, so i write the domain (-infinite, 5) U (5, infinite). it says this is a wrong answer.
 
logistic_guy said:
this is the question

Find the domain of f(x) = (x^2 - x - 6) / x - 5. there is no tap to write the square root so i write brackets (x^2 - x - 6).

it is clear 5 is the domain of the function. it keeps telling me wrong. i know 5 - 5 = 0 this is invalid in the fraction when it is written down.

there is no tap for infinite, so i write the domain (-infinite, 5) U (5, infinite). it says this is a wrong answer.
Click to expand...
Please tell us

the proper definition (include numerical example) of the domain of a function

according to your text book or class notes.
 
logistic_guy said:
Find the domain of f(x) = (x^2 - x - 6) / x - 5. there is no tap to write the square root so i write brackets (x^2 - x - 6).
Click to expand...
To express [imath]f(x)=\frac{\sqrt{x^2-x-6}}{x-5}[/imath] easily, you can write

f(x) = sqrt(x^2 - x - 6) / (x - 5)​

logistic_guy said:
it is clear 5 is the domain of the function. it keeps telling me wrong. i know 5 - 5 = 0 this is invalid in the fraction when it is written down.

there is no tap for infinite, so i write the domain (-infinite, 5) U (5, infinite). it says this is a wrong answer.
Click to expand...
The fact that the denominator is 0 when x is 5 means that 5 is not in the domain. Some students get confused by missing the fact that in solving x - 5 = 0, they are finding what is excluded, not what is included.

You appear to have ignored the square root you said is in the function. When is that not defined?

(The way you wrote this is fine.)
 
logistic_guy said:
this is the question

Find the domain of f(x) = (x^2 - x - 6) / x - 5. there is no tap to write the square root so i write brackets (x^2 - x - 6).

it is clear 5 is the domain of the function. it keeps telling me wrong. i know 5 - 5 = 0 this is invalid in the fraction when it is written down.

there is no tap for infinite, so i write the domain (-infinite, 5) U (5, infinite). it says this is a wrong answer.
Click to expand...
You say that the domain is 5, yet you write that the domain is (-infinite, 5) U (5, infinite). (-infinite, 5) U (5, infinite) includes all numbers except 5. So which is it, the domain is 5 or all numbers except 5?
Is one of these the answer? What can't/can you compute the square root of?
 
The best way to find the domain of a function is to first find the values that \(\displaystyle x\) can't be and then the domain is everything else (ie what \(\displaystyle x\) can be).

In the case of \(\displaystyle f(x) =\frac{ \sqrt{x^2 - x - 6}}{x - 5}\), you have the denominator to worry about (it can't be 0) as well as the bit under the square root sign (it can't be negative).

So, what value of \(\displaystyle x\) makes the denominator 0, and what values of \(\displaystyle x\) make the bit under the square root sign negative.

Your domain will be everything except these values.
 
Beer drenched reaction follows.
logistic_guy said:
this is the question

Find the domain of f(x) = (x^2 - x - 6) / x - 5. there is no tap to write the square root so i write brackets (x^2 - x - 6).

it is clear 5 is the domain of the function. it keeps telling me wrong. i know 5 - 5 = 0 this is invalid in the fraction when it is written down.

there is no tap for infinite, so i write the domain (-infinite, 5) U (5, infinite). it says this is a wrong answer.
Click to expand...
Another way to find the domain of a function, not necessarily the best way, is to consult the math demigod Desmos with an offering (preferably a fatted lamb). As they say, a picture is worth a thousand words.
www.desmos.com

logistic_guy i need to find the domain

www.desmos.com www.desmos.com
 
correct Dr.Peterson, the expression to my question \(\displaystyle \frac{\sqrt{x^2 - x - 6}}{x-5}\)

i'm understand the concept wrong. i thought if i solve for x, it is the domain

should i write the domain \(\displaystyle (-\infty, 4)(4,\infty)\)?

i don't know the proper definition of domain of function. i don't understant the drawing of function
 
logistic_guy said:
correct Dr.Peterson, the expression to my question \(\displaystyle \frac{\sqrt{x^2 - x - 6}}{x-5}\)

i'm understand the concept wrong. i thought if i solve for x, it is the domain

should i write the domain \(\displaystyle (-\infty, 4)(4,\infty)\)?

i don't know the proper definition of domain of function. i don't understant the drawing of function
Click to expand...
If the domain were all real numbers except 4, you would write \(\displaystyle (-\infty, 4)\cup(4,\infty)\). I assume 4 was a typo.

You haven't yet taken into account the radical. For what values of x is that undefined?
 
logistic_guy said:
i don't know the proper definition of domain of function.
Click to expand...
It was explained in #5; or you could search. Here's one textbook explanation with examples:

math.libretexts.org

4.7: Domain and Range of a Function

The domain of a function is all possible values of x that can be used as input to the function, which will result in a real number as the output. The range of a function is the set of all possible …
math.libretexts.org math.libretexts.org

logistic_guy said:
i don't understant the drawing of function
Click to expand...
Can you be more precise? What aspect of graphing do you have trouble with? And why do you think that's necessary here?
 
if 5 is not domain why not take a number less than 5? \(\displaystyle (-\infty, 4.9)\)? i do it \(\displaystyle (-\infty, 4)\) because i think decimal not accepted. before i did \(\displaystyle (-\infty, 5) \text{U} (5, \infty)\), it say wrong

if \(\displaystyle (-\infty, 5) \text{U} (5, \infty)\) wrong

if \(\displaystyle (-\infty, 4) \text{U} (4, \infty)\) wrong

it's because the square root?

Dr.Peterson, the graphing post 6. i say i don't understand graphing. i'm sorry i don't know what definition but i understand this The domain of a function is all possible values of x that can be used as input to the function, which will result in a real number as the output. The range of a function is the set of all possible output values of a function.

i'm an aritist, so i'm new to math. ican't tell what my textbook say about the definition
 
logistic_guy said:
i'm an aritist, so i'm new to math. ican't tell what my textbook say about the definition
Click to expand...
Your textbook should have an "index" in front-pages. Look-up the section where it begins to describe "function" and "domain" and "range". Read those pages carefully.

Better yet,
Your textbook should have an "glossary" in back-pages. Look-up the section where it begins to describe "function" and "domain" and "range". Read those pages carefully.

You are NOT new to math. You have learnt to count, add, subtract numbers. Those are the beginning drumbeats of math.
 
logistic_guy said:
where index and glossary? i can't find it
Click to expand...
We can't possibly tell you where to find things in your book(s) simply because we can't see your book(s)!

However, @khansaheb has mixed up his terminology somewhat so it may help you to search your book(s) if I explain that...

The Index is at the back (not the front) of a book and is a list of topics or terms included in the book with the relevant page numbers where those terms (or words) or topics can be found in the book.

The Contents of a book appear at the front and is a list of the topics addressed in the book (usually listed by Chapters).

A Glossary is an alphabetical list of topics or terms with a definition or explanation provided for each of them. If a book contains a glossary then that word (Glossary) will usually appear in both the contents and the index.

Not all books contain a glossary (unfortunately) but most technical publications will have both a contents section near the front and an index at the back.

If your book doesn't contain any of these things then I would suggest you get a better one (or simply read the reference you were already given at Post #10 (above).

Hope that helps. 😊
 
post 10 say The domain of a function is all possible values of x that can be used as input to the function, which will result in a real number as the output. The range of a function is the set of all possible output values of a function.

i already say i understand this
 
You must log in or register to reply here.
Top