Question

Please help! Will fan and medal!!!!!

Question attached in comments.

I think it is NOT in the domain

Answer 1

@DannyO19

Answer 2

So plugging in -6x+3 into your function f(x)..

Answer 3

What would you get?

Answer 4

-2

Answer 5

I agree with Danny that it's important that you form f(g(x)) using the two given functions. Only after you've done that are you ready to think about the domain of f(g(x)).

Answer 6

Your equation for f of g(x) So Sqrt of -6x+1

Answer 7

I get 2.44948-

Answer 8

You'd understand more if you would PLEASE form f(g(x)) from the given functions. Not being able to see what you've done, I can't give you meaningful feedback.

Answer 9

I literally did what he said. I did \[\sqrt{-6(-2+1)}\] just like he asked. All I'm ever doing is trying to fill in as I'm told you don't have to yell I'm already frustrated enough ._.

Answer 10

If f(x)=Sqrt(x-2) and g(x)=-6x-3, then

f(g(x)) =\[\sqrt{(-6x-3) -2}\]

Answer 11

which is quite different. Thank you for showing your work.

In \[f(x)=\sqrt{(x)-2}\]

Answer 12

Alright. So since that says domain error I was correct and it is not in the domain?

Answer 13

"x" shows up twice. Replace the first x by "g(x)" . Replace the 2nd x by (-6-3).

Answer 14

So then it is in the domain?

Answer 15

From your comments I see you are tired and just want to finish, even if you don't truly understand how we arrive at the correct answer. I'm sorry you're frustrated.

I ask you to simplify my expression for f(g(x)), shown above.

Answer 16

(-6x-3)-2=??

Answer 17

Well I did \[\sqrt{(-6*5-3)-2}\] and my calculator said domain error?

Answer 18

When i take away the sqrt i get -35

Answer 19

(-6*x-3)-2 comes out to -6x-5. Yes, if you evaluate this a t x= 5 you do get -35.

What is the domain of the sqrt function?

Next: Is 5 in that domain?

Answer 20

yes?

Answer 21

For me, the question is WHY?

the domain of the Sqrt function is [0, infinity].

is -35 a member of that set?

Answer 22

no

Answer 23

right. you get that -35 when you let x=5.

Since the that -35 is not within the domain of the sqrt functin, 5 is not in the domain of your f(g(x)).

Answer 24

It's asking if -5 is....

Answer 25

What do you think?
Evaluate Sqrt((-6*[-5]-2), please.

Answer 26

\[\sqrt{-6(-5)-2}=?\]

Answer 27

Note: you must do multiplication before adding or subtraction. Order of Operations rules.

Answer 28

I think no

Answer 29

Please evaluate the expression I've typed out for you. Multiply first, subtract 2nd.

Answer 30

30-2 = 28

Answer 31

is that within the domain of the Sqrt(x) function?

Answer 32

yes

Answer 33

The domain of the sqrt function is [0, inf] and 28 is within that domain. therefore,

-5 is part of the domain of your f(g(x)).

Answer 34

Still there? You have successfully worked thru this question. Congrats. Sorry it took so long. Take care, see you again.