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anonymous
 one year ago
Let f(x)=√4x and g(x) = x + 6. What's the smallest number that is in the domain of fog?
anonymous
 one year ago
Let f(x)=√4x and g(x) = x + 6. What's the smallest number that is in the domain of fog?

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Well, at least we know how to find fog now. Check if your answer matches mine for the fog part.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3\[f\circ g = f(g(x)) = \sqrt{4\cdot (x+6)}=\sqrt{4x + 24}\]

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0sqrt(4)*(x+6)

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0I think its not whole underoot

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok we're getting somewhere.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0Ya @Generalman1230 , what is it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hold on, give me a sec guys.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I just can't wrap it around my head. @jtvatsim @arindameducationusc

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought I had something

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3No worries, I think we are majoring on minors right now. The question that arindameducationusc doesn't have to do with the process I taught you. It's just a matter of "before we get carried away" let's check that we actually wrote the equation for f correctly.

arindameducationusc
 one year ago
Best ResponseYou've already chosen the best response.0@Generalman1230 , @jtvatsim will take care.... don't worry..... :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3OK, let's try this from the top again. I think you are fine. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3We have \[f(x) = \sqrt{4x}\] where the 4x is completely inside the root, and \[g(x) = x+6\].

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3We then know based on our previous conversation that \[f \circ g = f(g(x)) = f(x+6) = \sqrt{4 \cdot (x+6)} = \sqrt{4x + 24}\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3That's where we left off before. Are you OK up to that step?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Excellent. Now, the question wants us to find the smallest number in the domain. How small can I get before there is a problem? Well, let's experiment! Time for science!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Or even better, we can stop and think about what can and can't happen.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3The only issue in this situation (there are no fractions, so dividing by 0 isn't a problem) is if we get a negative number inside the square root.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3The smallest thing that can EVER be inside a square root is 0 then. It's the first "notnegative" number. Does that logic make sense so far?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Phew... got caught in an internet black hole there, don't know what happened.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The website crashed, I guess. I couldn't get on it for a second.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Yep, it's still a little shaky even now...

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3So, are you comfortable with the idea that the smallest thing you can have inside a square root is 0? There is one more step to do after coming to grips with this fact.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tried to type in yes, but the site crashed again.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3lol, almost there site, just hang in there.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3K, so I'll make this quick before it crashes again.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3The smallest thing that can be inside is 0. BUT... we have a HUGE equation inside right now. That's not a problem, the smallest this HUGE equation inside can be is 0, so... this means: 4x + 24 = 0 is the smallest we can go, 4x = 24 is the smallest we can go, x = 6 is the smallest we can go. x = 6 is the smallest number in the domain.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jtvatsim I can't thank you enough for all the help you gave throughout the past hour. I know you have to get off but could you help me with one more problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If you have to go now, then that's totally understandable.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Gotcha, you know I do have to run. But message me the question, and I can message you back sometime tomorrow. If it's due before then, there are plenty of other great tutors online. Good luck! You have come far! :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@jtvatsim Will do, thanks again.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3You are very welcome! Summit Mt. Math and conquer it! >:) Nights!
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