i need to find the domain

[logistic_guy]

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.

 

[khansaheb]

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.

Please tell us

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

according to your text book or class notes.

 

[Dr.Peterson]

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).

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)​

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.

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.)

 

[Steven G]

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.

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?

 

[Harry_the_cat]

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.

 

[jonah2.0]

Beer drenched reaction follows.

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.

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.

logistic_guy i need to find the domain

www.desmos.com

 

[logistic_guy]

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

 

[Dr.Peterson]

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

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?

 

[khansaheb]

i don't know the proper definition of domain of function

What does your textbook/class-notes say?

 

[Dr.Peterson]

i don't know the proper definition of domain of function.

It was explained in #5; or you could search. Here's one textbook explanation with examples:

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

i don't understant the drawing of function

Can you be more precise? What aspect of graphing do you have trouble with? And why do you think that's necessary here?