Question

Which value of t is NOT in the domain of the function G(t)=\(36)/(6 t-25)?
please explain

Answer 1

I see that the denominator of the function is 6t-25
Would you agree that the denominator cannot be 0?

Answer 2

yes, nor divided by 0 correct? according to my professor, however nothing times 6 = 25
which is where I get lost

Answer 3

The denominator is 6t-25
The denominator cannot be 0
Therefore
\[6t-25\neq 0\]
\[6t \neq 25\]
\[t \neq \frac{25}{6}\]

Answer 4

And so 25/6 is not in the domain of the function

Answer 5

can you explain this process please?

Answer 6

Sorry if its a hassle just don't want to be posting every 5 seconds on here you know what I mean?

Answer 7

The process is:
Step 1: Identify the denominator of the function
Step 2: Set the denominator equal to zero
Step 3: Solve that equation
Step 4: Restrict the domain so that it does not contain that solution.

Answer 8

Therefore leaving the top, and using only the denominator? hence the 25/6 now, when you say set the denominator to zero are you looking for an answer that will equal it out to be zero?

Answer 9

yes.

Answer 10

In your problem replace t with 25/6 and see what happens.

Answer 11

I got it correct, now my next question not sure if you have time for this one so, Find the domain of the function f(x) = 3 x + 8 I got (1,11) how do you find out if it is (-oo,oo) for example closed point and open point on the graph?

Answer 12

Do you know what is meant by the domain?

Answer 13

I do not.

Answer 14

Therein lies your problem.
The domain of a function is all the numbers that are "legal" replacements for x.

Answer 15

what do you mean by legal replacement for x? I have an issue with the all real numbers what is meant by that to me all numbers are real because every number can be placed on the number line. Is that not true?

Answer 16

And why would some numbers be "illegal" you ask.
The answer is: two reasons:
1. Some numbers might cause the denominator to be 0 which is undefined
2. Some numbers might cause the radicand, of a radical whose index is even, to be negative. That too is undefined.

Answer 17

can you explain point number 2 please?

Answer 18

\[f(x)=\sqrt[4]{x+6}\]

Answer 19

Supposing x is -13, what would the radicand be?

Answer 20

I never heard of a radicand before, but i'm guessing 4?

Answer 21

The index is 4. The radicand is the number under the radical

Answer 22

index being the number on the outside?

Answer 23

Did you see where I typed that the index is 4 in that example?

Answer 24

yes, however i'm not familiar with index radicand and radicals so i'm trying to piece it together