Question

Don't know how to do this help for medal

Answer 1

question

Answer 2

Which value of x is NOT in the domain of the function f(x)=\(23)/(11 x-24)? x=____

Answer 3

You cannot divide by zero. So if the denominator 11x-24 were equal to zero, then what must the value of x be?

Answer 4

so 0 is the value of x not in the domain?

Answer 5

try plugging x = 0 into f(x). Do you run into a division by zero error?

Answer 6

no

Answer 7

so x = 0 is a perfectly valid input

Answer 8

x = 0 is part of the domain

Answer 9

you need to solve 11x-24 = 0 for x to get the value of x that makes the denominator zero

Answer 10

24/11

Answer 11

@jim_thompson5910

Answer 12

correct, x = 24/11 is the value that when you plug it into 11x - 24, it turns into 0 causing the division by zero error

Answer 13

to avoid division by zero errors, we kick out any values of x that cause the division by zero errors.

So that's why x = 24/11 is not in the domain

Answer 14

Find the domain of f(x) = sqrt(4 x -5)

Answer 15

is it 5?

Answer 16

now you need to make sure that the radicand is never negative

Answer 17

so force it to be either 0 or positive

\[\Large 4x - 5 \ge 0\]

solve for x

Answer 18

x=5/4??

Answer 19

how do you write it in interval notation?

Answer 20

it's actually

\[\Large x \ge \frac{5}{4}\]

when you solve for x

Answer 21

and how would that be written in interval notion?

Answer 22

go ahead and write out what you think it looks like and I'll help you from there (if you need any). I want to see how much you know about interval notation.

Answer 23

(0,5/4)

Answer 24

the left most edge of the interval \(\Large x \ge \frac{5}{4}\) is 5/4, agreed?

Answer 25

I don't get it

Answer 26

\[\Large x \ge \frac{5}{4}\]

describes all the numbers that are greater than or equal to 5/4

Answer 27

the smallest that x can be is 5/4. It cannot get any smaller. So the left edge is 5/4

x can get as large as it wants, so the right edge is infinity

Answer 28

\[\Large x \ge \frac{5}{4}\]

written in interval notation is

\[\Large \left[\frac{5}{4},\infty)\right.\]