## 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?

1. jtvatsim

Well, at least we know how to find fog now. Check if your answer matches mine for the fog part.

2. jtvatsim

$f\circ g = f(g(x)) = \sqrt{4\cdot (x+6)}=\sqrt{4x + 24}$

3. arindameducationusc

sqrt(4)*(x+6)

4. arindameducationusc

I think its not whole underoot

5. anonymous

Ok we're getting somewhere.

6. arindameducationusc

Ya @Generalman1230 , what is it?

7. anonymous

Hold on, give me a sec guys.

8. anonymous

Sorry, I just can't wrap it around my head. @jtvatsim @arindameducationusc

9. anonymous

10. jtvatsim

No 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.

11. arindameducationusc

@Generalman1230 , @jtvatsim will take care.... don't worry..... :)

12. jtvatsim

OK, let's try this from the top again. I think you are fine. :)

13. jtvatsim

We have $f(x) = \sqrt{4x}$ where the 4x is completely inside the root, and $g(x) = x+6$.

14. jtvatsim

We then know based on our previous conversation that $f \circ g = f(g(x)) = f(x+6) = \sqrt{4 \cdot (x+6)} = \sqrt{4x + 24}$

15. jtvatsim

That's where we left off before. Are you OK up to that step?

16. anonymous

Yes, I am.

17. jtvatsim

Excellent. 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!

18. jtvatsim

Or even better, we can stop and think about what can and can't happen.

19. jtvatsim

The 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.

20. jtvatsim

The smallest thing that can EVER be inside a square root is 0 then. It's the first "not-negative" number. Does that logic make sense so far?

21. jtvatsim

Phew... got caught in an internet black hole there, don't know what happened.

22. anonymous

The website crashed, I guess. I couldn't get on it for a second.

23. jtvatsim

Yep, it's still a little shaky even now...

24. jtvatsim

So, 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.

25. anonymous

I tried to type in yes, but the site crashed again.

26. jtvatsim

lol, almost there site, just hang in there.

27. jtvatsim

K, so I'll make this quick before it crashes again.

28. jtvatsim

The 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.

29. anonymous

@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?

30. anonymous

If you have to go now, then that's totally understandable.

31. jtvatsim

Gotcha, 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! :)

32. anonymous

@jtvatsim Will do, thanks again.

33. jtvatsim

You are very welcome! Summit Mt. Math and conquer it! >:) Nights!