Question

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?

Answer 1

Is This Algebra 2?

Answer 2

yep

Answer 3

F(a) = a/8

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

F(50) = ???

Answer 4

6.25?

Answer 5

yes

Answer 6

`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

Answer 7

oh ok. and how about this?

Answer 8

theres another part

Answer 9

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

Answer 10

Would the range be x> than the number?

Answer 11

what are some possible values for 'a' ?

Answer 12

50... 6.25...?

Answer 13

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

Answer 14

a = 8?

Answer 15

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

Answer 16

oh, really?

Answer 17

so the domain is x>0

Answer 18

Yeah He's right

Answer 19

yeah \(\Large a \ge 0\)

Answer 20

Oh yeah

Answer 21

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

Answer 22

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

Answer 23

Yeah I Believe The Domain Is X > 0

Answer 24

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

Answer 25

would this be like a(m)?

Answer 26

in terms of meters?

Answer 27

i guess... It doesn't really say

Answer 28

it seems like there's something missing but idk what

Answer 29

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

Answer 30

maybe they just want you to convert to meters

Answer 31

1 mile = 1609.34 meters (approximate)

Answer 32

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

Answer 33

1 mile = 1609.34 meters (approximate)

a*1 mile = a*1609.34 meters .... Multiply both sides by a.

a miles = 1609.34a meters

Answer 34

I am so confused...

Answer 35

I think (a)(m)

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

yeah... Ugh, this is so aggravating

Answer 40

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

Answer 41

alright

Answer 42

Thank you for your help so far though!!

Answer 43

no problem

Answer 44

@Mertsj

Answer 45

You rang?

Answer 46

Yes, thank you

Answer 47

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

Answer 48

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

Answer 49

yes

Answer 50

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

Answer 51

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

Answer 52

ok, I didn't think that was really important

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

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).

Answer 58

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

Answer 59

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

Answer 60

So we might say here is a map:

Answer 61

Oh ok. So 50 is a? correct?