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?

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- anonymous

Is This Algebra 2?

- anonymous

yep

- jim_thompson5910

F(a) = a/8
F(50) = 50/8 ... replace each 'a' with 50
F(50) = ???

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## More answers

- anonymous

6.25?

- jim_thompson5910

yes

- 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

oh ok. and how about this?

- anonymous

theres another part

- anonymous

What are the units for the domain and range of the function? What is the domain and range for the function?

- anonymous

Would the range be x> than the number?

- jim_thompson5910

what are some possible values for 'a' ?

- anonymous

50... 6.25...?

- jim_thompson5910

a = 50 is one value, what's another?

- anonymous

a = 8?

- 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

oh, really?

- anonymous

so the domain is x>0

- anonymous

Yeah He's right

- jim_thompson5910

yeah \(\Large a \ge 0\)

- anonymous

Oh yeah

- anonymous

I forgot the equal to part... Do you think you could help me with two more parts?

- jim_thompson5910

'a' is the input variable (not x this time)
remember to underline the `>`

- anonymous

Yeah I Believe The Domain Is X > 0

- anonymous

Find the a in terms of m and lable this new function G. Tell what this function represents?

- anonymous

would this be like a(m)?

- jim_thompson5910

in terms of meters?

- anonymous

i guess... It doesn't really say

- jim_thompson5910

it seems like there's something missing but idk what

- anonymous

It just says find a in terms of m and label this new function G. Tell what this function represents.

- jim_thompson5910

maybe they just want you to convert to meters

- jim_thompson5910

1 mile = 1609.34 meters (approximate)

- anonymous

No, but I think it's just asking for a in terms of m. This is like functions and inverses

- 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

I am so confused...

- anonymous

I think (a)(m)

- anonymous

Ok.. Let's try last part then. Determine if F and G are inverses

- anonymous

But for that we need to find out what a is in terms of m.... :(

- jim_thompson5910

yeah I'm not sure what they want for g(x)

- anonymous

yeah... Ugh, this is so aggravating

- anonymous

Let me see if I can figure it out, and If I still can't I'll call you back.. Ok..?

- jim_thompson5910

alright

- anonymous

Thank you for your help so far though!!

- jim_thompson5910

no problem

- anonymous

- Mertsj

You rang?

- anonymous

Yes, thank you

- anonymous

I just don't get this question... Do you mind leading me through it?

- Mertsj

Not at all. You found that the f(50)=6.25, right?

- anonymous

yes

- anonymous

But from there, I just sorta lost it... I don't get the find a in terms of m thing

- Mertsj

Notice that the problem says that the function gives the distance in inches on a map.

- anonymous

ok, I didn't think that was really important

- Mertsj

So 6.25 is the distance in inches on a map. Big deal you say.

- anonymous

Ok. I get that much but then I don't

- Mertsj

And you have a point however, the second part of the question wants an explanation of the significance of 6.25 inches.

- anonymous

Oh ok. Isn't the significance of it, the fact that you need it to be able to find G

- 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

Like, isn't the 6.25 the value of a? Or have I mistaken this entire thing....?

- anonymous

So what can I do to find the domain and range?

- Mertsj

So we might say here is a map:|dw:1443834662965:dw|

- anonymous

Oh ok. So 50 is a? correct?

- Mertsj

yes

- anonymous

Ok, and would that be the range...?

- Mertsj

50 miles takes 6.25 inches on the map.

- anonymous

ok

- 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

Yes. so the range would be any number greater than or equal to zero?

- 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

Oh ok. And how can I find the range?

- 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

We would not include 0. Why would we want to represent 0 miles on a map?

- anonymous

So the range would be x>0

- Mertsj

yes

- anonymous

Oh ok. So the domain is x=>0 and the range is x>0

- Mertsj

Did you notice what I said about representing 0 miles on a map?

- anonymous

What is the difference between the "units for the domain and range" and "what is teh domain and range"

- anonymous

*the

- 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

Oh that's what the units represent? Correct?

- Mertsj

The units ARE miles and inches.

- 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

No. a is the number of miles. Would it be easier for you to use x and y?

- anonymous

yes please.. all these variables give me a headache.

- Mertsj

Or maybe m for miles and i for inches. We would say that inches = miles/8

- Mertsj

Or i = m/8

- anonymous

Ok, so 6.25=50/8

- Mertsj

If we want miles in terms of inches we would say miles = 8(inches)

- anonymous

so 50=8

- anonymous

since 50 is the miles?

- Mertsj

See? inches= miles divided by 8 and miles = inches times 8

- anonymous

so 6.26=50/8 and 50=6.26/8

- Mertsj

But your problem uses "a" for miles and f(a) for inches

- Mertsj

6.25 = 50/8 and 50 = 8(6.25)

- anonymous

oh right

- Mertsj

f(a)= a/8 and a = 8(f(a))

- anonymous

Oh ok. would that be the function?

- anonymous

Where is the m though?

- Mertsj

m = f(a) so you can replace f(a) with m

- Mertsj

m=a/8 and a = 8m

- anonymous

ok, and that would still be the same thing?

- Mertsj

Yes. In math if two quantities are equal, you can replace one with the other.

- 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

I don't know where you are getting G.

- Mertsj

I don't see it anywhere in the problem you posted.

- anonymous

Well the new function must be named G. At least that's what the problem tells me.

- anonymous

Find a in terms of m and label this new function G

- Mertsj

Perhaps you should post the entire problem

- anonymous

I did. Its a bit farther up. Like in pieces. I am sorry

- 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

So a in terms of m is a=8m and the problem said to label this g. So we have g(m)=8m

- 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

yes.

- anonymous

Ok, and how about the whole inverse thing?

- anonymous

I-am spus , ce tot vorbești ? Acest lucru pare complet ... nu contează . Voi taci acum .

- 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

I am sorry @SweetBeat but I am afraid we don't understand your question...

- anonymous

and oh ok

- anonymous

Oh, right they both have to be the same thing right?

- 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

Oh ok. I was wondering who was doing that.

- Mertsj

Yes. The way to find an inverse function is to interchange the variables.

- anonymous

Thank you so much @Mertsj for all of your help!! i understand this much better now!!!

- Mertsj

So the inverse of m= a/8 is a = m/8

- anonymous

Thank you, than you *bows in a grateful manner*

- anonymous

Oh yeah you just switch them

- Mertsj

you're very welcome. Good luck.

- 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

I just got confused on that one part

- 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

Ok. Thank you!

- Mertsj

yw

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