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Is This Algebra 2?
F(a) = a/8 F(50) = 50/8 ... replace each 'a' with 50 F(50) = ???
`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
oh ok. and how about this?
theres another part
What are the units for the domain and range of the function? What is the domain and range for the function?
Would the range be x> than the number?
what are some possible values for 'a' ?
a = 50 is one value, what's another?
a = 8?
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
so the domain is x>0
Yeah He's right
yeah \(\Large a \ge 0\)
I forgot the equal to part... Do you think you could help me with two more parts?
'a' is the input variable (not x this time) remember to underline the `>`
Yeah I Believe The Domain Is X > 0
Find the a in terms of m and lable this new function G. Tell what this function represents?
would this be like a(m)?
in terms of meters?
i guess... It doesn't really say
it seems like there's something missing but idk what
It just says find a in terms of m and label this new function G. Tell what this function represents.
maybe they just want you to convert to meters
1 mile = 1609.34 meters (approximate)
No, but I think it's just asking for a in terms of m. This is like functions and inverses
1 mile = 1609.34 meters (approximate) a*1 mile = a*1609.34 meters .... Multiply both sides by a. a miles = 1609.34a meters
I am so confused...
I think (a)(m)
Ok.. Let's try last part then. Determine if F and G are inverses
But for that we need to find out what a is in terms of m.... :(
yeah I'm not sure what they want for g(x)
yeah... Ugh, this is so aggravating
Let me see if I can figure it out, and If I still can't I'll call you back.. Ok..?
Thank you for your help so far though!!
Yes, thank you
I just don't get this question... Do you mind leading me through it?
Not at all. You found that the f(50)=6.25, right?
But from there, I just sorta lost it... I don't get the find a in terms of m thing
Notice that the problem says that the function gives the distance in inches on a map.
ok, I didn't think that was really important
So 6.25 is the distance in inches on a map. Big deal you say.
Ok. I get that much but then I don't
And you have a point however, the second part of the question wants an explanation of the significance of 6.25 inches.
Oh ok. Isn't the significance of it, the fact that you need it to be able to find G
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).
Like, isn't the 6.25 the value of a? Or have I mistaken this entire thing....?
So what can I do to find the domain and range?
So we might say here is a map:|dw:1443834662965:dw|
Oh ok. So 50 is a? correct?
Ok, and would that be the range...?
50 miles takes 6.25 inches on the map.
So if a is a number of miles on a map, then a would have to be some positive number, would it not?
Yes. so the range would be any number greater than or equal to zero?
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.
Oh ok. And how can I find the range?
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.
We would not include 0. Why would we want to represent 0 miles on a map?
So the range would be x>0
Oh ok. So the domain is x=>0 and the range is x>0
Did you notice what I said about representing 0 miles on a map?
What is the difference between the "units for the domain and range" and "what is teh domain and range"
"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.
Oh that's what the units represent? Correct?
The units ARE miles and inches.
Oh wait. To find a in terms of m, would I set it up like this? 50=f(6.25)=6.25/8
No. a is the number of miles. Would it be easier for you to use x and y?
yes please.. all these variables give me a headache.
Or maybe m for miles and i for inches. We would say that inches = miles/8
Or i = m/8
Ok, so 6.25=50/8
If we want miles in terms of inches we would say miles = 8(inches)
since 50 is the miles?
See? inches= miles divided by 8 and miles = inches times 8
so 6.26=50/8 and 50=6.26/8
But your problem uses "a" for miles and f(a) for inches
6.25 = 50/8 and 50 = 8(6.25)
f(a)= a/8 and a = 8(f(a))
Oh ok. would that be the function?
Where is the m though?
m = f(a) so you can replace f(a) with m
m=a/8 and a = 8m
ok, and that would still be the same thing?
Yes. In math if two quantities are equal, you can replace one with the other.
Oh cool, thanks! and are they both inverses? F and G? I would think so because inverses must both be equal to x, right?
I don't know where you are getting G.
I don't see it anywhere in the problem you posted.
Well the new function must be named G. At least that's what the problem tells me.
Find a in terms of m and label this new function G
Perhaps you should post the entire problem
I did. Its a bit farther up. Like in pieces. I am sorry
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
So a in terms of m is a=8m and the problem said to label this g. So we have g(m)=8m
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?
Ok, and how about the whole inverse thing?
I-am spus , ce tot vorbești ? Acest lucru pare complet ... nu contează . Voi taci acum .
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.
I am sorry @SweetBeat but I am afraid we don't understand your question...
and oh ok
Oh, right they both have to be the same thing right?
@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.
Oh ok. I was wondering who was doing that.
Yes. The way to find an inverse function is to interchange the variables.
Thank you so much @Mertsj for all of your help!! i understand this much better now!!!
So the inverse of m= a/8 is a = m/8
Thank you, than you *bows in a grateful manner*
Oh yeah you just switch them
you're very welcome. Good luck.
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
I just got confused on that one part
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.
Ok. Thank you!