anonymous
  • anonymous
The function m = F(a) = a/8 gives the distance in inches on a map between two points that are actually a miles apart. 1. Whats if F(50)? What does F(50) represent?
Mathematics
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anonymous
  • anonymous
The function m = F(a) = a/8 gives the distance in inches on a map between two points that are actually a miles apart. 1. Whats if F(50)? What does F(50) represent?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Is This Algebra 2?
anonymous
  • anonymous
yep
jim_thompson5910
  • jim_thompson5910
F(a) = a/8 F(50) = 50/8 ... replace each 'a' with 50 F(50) = ???

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anonymous
  • anonymous
6.25?
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
`The function m = F(a) = a/8 gives the distance in inches on a map between two points that are actually a miles apart` so basically, whatever the value of 'a' is, the output F(a) tells us the distance on the paper map so in this case, a = 50 miles means F(a) = 6.25 inches 6.25 inches on the map corresponds to 50 miles in real life
anonymous
  • anonymous
oh ok. and how about this?
anonymous
  • anonymous
theres another part
anonymous
  • anonymous
What are the units for the domain and range of the function? What is the domain and range for the function?
anonymous
  • anonymous
Would the range be x> than the number?
jim_thompson5910
  • jim_thompson5910
what are some possible values for 'a' ?
anonymous
  • anonymous
50... 6.25...?
jim_thompson5910
  • jim_thompson5910
a = 50 is one value, what's another?
anonymous
  • anonymous
a = 8?
jim_thompson5910
  • jim_thompson5910
sure, we could have some distance be 8 miles we could also have 2 miles, 1.5 miles, 99 miles basically any positive number or 0
anonymous
  • anonymous
oh, really?
anonymous
  • anonymous
so the domain is x>0
anonymous
  • anonymous
Yeah He's right
jim_thompson5910
  • jim_thompson5910
yeah \(\Large a \ge 0\)
anonymous
  • anonymous
Oh yeah
anonymous
  • anonymous
I forgot the equal to part... Do you think you could help me with two more parts?
jim_thompson5910
  • jim_thompson5910
'a' is the input variable (not x this time) remember to underline the `>`
anonymous
  • anonymous
Yeah I Believe The Domain Is X > 0
anonymous
  • anonymous
Find the a in terms of m and lable this new function G. Tell what this function represents?
anonymous
  • anonymous
would this be like a(m)?
jim_thompson5910
  • jim_thompson5910
in terms of meters?
anonymous
  • anonymous
i guess... It doesn't really say
jim_thompson5910
  • jim_thompson5910
it seems like there's something missing but idk what
anonymous
  • anonymous
It just says find a in terms of m and label this new function G. Tell what this function represents.
jim_thompson5910
  • jim_thompson5910
maybe they just want you to convert to meters
jim_thompson5910
  • jim_thompson5910
1 mile = 1609.34 meters (approximate)
anonymous
  • anonymous
No, but I think it's just asking for a in terms of m. This is like functions and inverses
jim_thompson5910
  • jim_thompson5910
1 mile = 1609.34 meters (approximate) a*1 mile = a*1609.34 meters .... Multiply both sides by a. a miles = 1609.34a meters
anonymous
  • anonymous
I am so confused...
anonymous
  • anonymous
I think (a)(m)
anonymous
  • anonymous
Ok.. Let's try last part then. Determine if F and G are inverses
anonymous
  • anonymous
But for that we need to find out what a is in terms of m.... :(
jim_thompson5910
  • jim_thompson5910
yeah I'm not sure what they want for g(x)
anonymous
  • anonymous
yeah... Ugh, this is so aggravating
anonymous
  • anonymous
Let me see if I can figure it out, and If I still can't I'll call you back.. Ok..?
jim_thompson5910
  • jim_thompson5910
alright
anonymous
  • anonymous
Thank you for your help so far though!!
jim_thompson5910
  • jim_thompson5910
no problem
anonymous
  • anonymous
Mertsj
  • Mertsj
You rang?
anonymous
  • anonymous
Yes, thank you
anonymous
  • anonymous
I just don't get this question... Do you mind leading me through it?
Mertsj
  • Mertsj
Not at all. You found that the f(50)=6.25, right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
But from there, I just sorta lost it... I don't get the find a in terms of m thing
Mertsj
  • Mertsj
Notice that the problem says that the function gives the distance in inches on a map.
anonymous
  • anonymous
ok, I didn't think that was really important
Mertsj
  • Mertsj
So 6.25 is the distance in inches on a map. Big deal you say.
anonymous
  • anonymous
Ok. I get that much but then I don't
Mertsj
  • Mertsj
And you have a point however, the second part of the question wants an explanation of the significance of 6.25 inches.
anonymous
  • anonymous
Oh ok. Isn't the significance of it, the fact that you need it to be able to find G
Mertsj
  • Mertsj
And the problem tells us that as well when it says that 6.25 inches is the distance on the map of two cities that are "a" miles apart and "a" in our problem is 50 because our function is f(a)=a/8 and we found f(50).
anonymous
  • anonymous
Like, isn't the 6.25 the value of a? Or have I mistaken this entire thing....?
anonymous
  • anonymous
So what can I do to find the domain and range?
Mertsj
  • Mertsj
So we might say here is a map:|dw:1443834662965:dw|
anonymous
  • anonymous
Oh ok. So 50 is a? correct?
Mertsj
  • Mertsj
yes
anonymous
  • anonymous
Ok, and would that be the range...?
Mertsj
  • Mertsj
50 miles takes 6.25 inches on the map.
anonymous
  • anonymous
ok
Mertsj
  • Mertsj
So if a is a number of miles on a map, then a would have to be some positive number, would it not?
anonymous
  • anonymous
Yes. so the range would be any number greater than or equal to zero?
Mertsj
  • Mertsj
And that is the domain: the positive real numbers. Similarly, if you divide a positive real number by 8 you get a positive real number so the range is also the set of positive real numbers.
anonymous
  • anonymous
Oh ok. And how can I find the range?
Mertsj
  • Mertsj
Did you read my previous post? Similarly, if you divide a positive real number by 8 you get a positive real number so the range is also the set of positive real numbers.
Mertsj
  • Mertsj
We would not include 0. Why would we want to represent 0 miles on a map?
anonymous
  • anonymous
So the range would be x>0
Mertsj
  • Mertsj
yes
anonymous
  • anonymous
Oh ok. So the domain is x=>0 and the range is x>0
Mertsj
  • Mertsj
Did you notice what I said about representing 0 miles on a map?
anonymous
  • anonymous
What is the difference between the "units for the domain and range" and "what is teh domain and range"
anonymous
  • anonymous
*the
Mertsj
  • Mertsj
"a" represents the members of the domain. According to the problem those numbers represent MILES between cities. f(a) represents the members of the range. According to the problem those numbers represent INCHES on the map.
anonymous
  • anonymous
Oh that's what the units represent? Correct?
Mertsj
  • Mertsj
The units ARE miles and inches.
anonymous
  • anonymous
Oh wait. To find a in terms of m, would I set it up like this? 50=f(6.25)=6.25/8
Mertsj
  • Mertsj
No. a is the number of miles. Would it be easier for you to use x and y?
anonymous
  • anonymous
yes please.. all these variables give me a headache.
Mertsj
  • Mertsj
Or maybe m for miles and i for inches. We would say that inches = miles/8
Mertsj
  • Mertsj
Or i = m/8
anonymous
  • anonymous
Ok, so 6.25=50/8
Mertsj
  • Mertsj
If we want miles in terms of inches we would say miles = 8(inches)
anonymous
  • anonymous
so 50=8
anonymous
  • anonymous
since 50 is the miles?
Mertsj
  • Mertsj
See? inches= miles divided by 8 and miles = inches times 8
anonymous
  • anonymous
so 6.26=50/8 and 50=6.26/8
Mertsj
  • Mertsj
But your problem uses "a" for miles and f(a) for inches
Mertsj
  • Mertsj
6.25 = 50/8 and 50 = 8(6.25)
anonymous
  • anonymous
oh right
Mertsj
  • Mertsj
f(a)= a/8 and a = 8(f(a))
anonymous
  • anonymous
Oh ok. would that be the function?
anonymous
  • anonymous
Where is the m though?
Mertsj
  • Mertsj
m = f(a) so you can replace f(a) with m
Mertsj
  • Mertsj
m=a/8 and a = 8m
anonymous
  • anonymous
ok, and that would still be the same thing?
Mertsj
  • Mertsj
Yes. In math if two quantities are equal, you can replace one with the other.
anonymous
  • anonymous
Oh cool, thanks! and are they both inverses? F and G? I would think so because inverses must both be equal to x, right?
Mertsj
  • Mertsj
I don't know where you are getting G.
Mertsj
  • Mertsj
I don't see it anywhere in the problem you posted.
anonymous
  • anonymous
Well the new function must be named G. At least that's what the problem tells me.
anonymous
  • anonymous
Find a in terms of m and label this new function G
Mertsj
  • Mertsj
Perhaps you should post the entire problem
anonymous
  • anonymous
I did. Its a bit farther up. Like in pieces. I am sorry
anonymous
  • anonymous
This is what it says. The function m=f(a) = a/8 give the distance in inches on a map between two points that are actually a miles apart. What is f(50)? What does F(50) represent? What are the units for the domain and range of the new function? What is the domain and range of the new function? Find a in terms of m and lable this new function G. Tell what this function represents. Determine if F and G are inverses
Mertsj
  • Mertsj
So a in terms of m is a=8m and the problem said to label this g. So we have g(m)=8m
anonymous
  • anonymous
Oooh. Oh wow, that is what I had originally but I erased it because I thought it was wrong... And this would represent the number of miles, right?
Mertsj
  • Mertsj
yes.
anonymous
  • anonymous
Ok, and how about the whole inverse thing?
anonymous
  • anonymous
I-am spus , ce tot vorbești ? Acest lucru pare complet ... nu contează . Voi taci acum .
Mertsj
  • Mertsj
If you replace the variable in the function f with x you will get f(x)=x/8. If you replace the variable in the function g with x you will get g(x)=8x. According to the definition of inverse functions, you would get the same thing if they were inverses. We don't get the same thing so they are not inverse functions.
anonymous
  • anonymous
I am sorry @SweetBeat but I am afraid we don't understand your question...
anonymous
  • anonymous
and oh ok
anonymous
  • anonymous
Oh, right they both have to be the same thing right?
Mertsj
  • Mertsj
@SweetBeat Neither of us know the language you are posting in so we find it very distracting and that is why I keep deleting your posts.
anonymous
  • anonymous
Oh ok. I was wondering who was doing that.
Mertsj
  • Mertsj
Yes. The way to find an inverse function is to interchange the variables.
anonymous
  • anonymous
Thank you so much @Mertsj for all of your help!! i understand this much better now!!!
Mertsj
  • Mertsj
So the inverse of m= a/8 is a = m/8
anonymous
  • anonymous
Thank you, than you *bows in a grateful manner*
anonymous
  • anonymous
Oh yeah you just switch them
Mertsj
  • Mertsj
you're very welcome. Good luck.
anonymous
  • anonymous
One more question... I apologize. But the domain and range would be the x>0 (domain in miles) and x=>0 (range in inches) right? @Mertsj
anonymous
  • anonymous
I just got confused on that one part
Mertsj
  • Mertsj
Yes. Very good but typically we use y for range. You might want to use a for domain and m for range since those are the variables used in your problem.
anonymous
  • anonymous
Ok. Thank you!
Mertsj
  • Mertsj
yw

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