Question

@jim_thompson5910 Last one! :)

Answer 1

range = set of all possible outputs = set of all possible y values

Answer 2

My bad, wrong question!

Answer 3

(f-g)(5) = f(5) - g(5) = ???

Answer 4

I don't understand what is "f" and what is "g" here..
I know you are supposed to add somewhere, I believe.

Answer 5

f(5) is the y value when x = 5 for the f(x) function

Answer 6

also, f(5) is the value of f(x) when x = 5

Answer 7

f alone is not a variable

it's a function

Answer 8

@lilia222 check the charts and on the top left corner of the chart there is f(x) and g(x)
and how jim told you f(5) - g(5) = ?

Answer 9

to find f(5), you look in the f(x) table

locate the row that has x = 5
the value in the column right next to it is the value of f(5)

Answer 10

You need to find function equations for these to make it easier to understand, lilia222?

Answer 11

Maybe I can help by helping you find the equations f(x) and g(x)...it would model more closely, then, what you have been doing thus far...

Answer 12

woah.. okay, I don't understand because in this problem they don't tell you f(x)=
or g(x) = . All they tell you is x=5 , so I'm a bit lost...

Answer 13

See attached and it may help

Answer 14

f(x) is just another of saying the following equation. So f(x) in this case is a function that when x=-5 and the results is -11. Basically saying for some undescribed equation f that has variable x, when x =-5 the equation results in -11.

Answer 15

145-65=80

Answer 16

how?

Answer 17

what is 29 - 13 =?

Answer 18

@lilia222 Does that help? The same goes for the g function. So when you see (f-g)(5). It is saying look at function f(5) and subtract function g(5) from it.

Answer 19

you dont have to multiply

Answer 20

you don't multiply 5 and 29 to get 145

you simply use 29 as the value of f(5)

ie, f(5) = 29

Answer 21

lilia222...I CAN HELP YOU FIND THE FUNCTION EQUATIONS IF YOU'D LIKE, MY DEAR!

Answer 22

This could be so much simpler for you...

Answer 23

f(x)= f(5) = 29(5) = 145?
@IMStuck .. please , I'm semi- lost right now.

Answer 24

the function notation is throwing you off

Answer 25

they just want you to subtract the y values of each table when x = 5

Answer 26

Ok, taking the tables one at a time...the first thing you want to do is to write equations for these functions because that is what you have been doing all along, is working with composite functions, right? Where they already gave you the function.

Answer 27

Okay and yes.

Answer 28

Looking at the tables, you can write the equations from the info they gave you. The x is the "x" and the f(x0 is the y. The first thing you have to do is remember the point-slope form of an equation, which is \[y-_{1}=m(x-x _{1})\]where m is the slope. You can find your slope by using the points on the table. The slope formula is \[\frac{ y _{2} -y _{1}}{ x _{2}-x _{1} }\]Start with the first two y points and the first two x points to find the slope.

Answer 29

\[\frac{ 1-(-11) }{ -2-(-5) }=\frac{ 1+11 }{ -2+5 }=\frac{ 12 }{ 3}=4\]If you do that with the second and third values of y and x you will also see that the slope is 4. So m = 4 in our point-slope equation. Now pick a point for you y1 and x1. I picked (1, 13) because they are both positive. Fill in your equation now with the slope value of 4 and your point (1, 13):

Answer 30

@IMStuck where are you trying to get to?

Answer 31

\[y-13=4(x-1)\]Solving this for y you get y = 4x + 9. Or in terms of f(x), you get
f(x) = 4x + 9. That is your f(x) function. Now let's find g(x) the same way, by finding first the slope and then the equation.

Answer 32

... oh Lord; could math just die right now.. like now now >.<

Answer 33

The slope of the function g(x) is 2, and picking a point (5, 13), your equation is
g(x) = 2x + 3. Now subtract f(x) - g(x) when x is 5.

Answer 34

\[4(5) +9-(2(5)+3)=29-13=16\]

Answer 35

There...that's your answer.

Answer 36

@lilia222 See if this helps. I just made it for you.

Answer 37

I got to the answer, mrfriedrice, the answer!

Answer 38

you actually didnt have to do that much work but bravo!!!!

Answer 39

This is becoming a lot more complicated than it has to be.

when x = 5, y = 29 for the first table. So f(5) = 29
when x = 5, y = 13 for the second table. So g(5) = 13

Now subtract the two y values: f(5) - g(5) = 29 - 13 = 16

So, (f-g)(5) = 16

Answer 40

That's all you have to do. Look at the table and find the outputs of the functions when the inputs are x = 5. Then subtract those outputs (f - g)

Answer 41

The attachment shows what I mean (the first part)

Answer 42

jim_thompson5910, you are brilliant, sir. However, I think lilia222 was so stuck on the composites the way she was used to seeing them, in equation form, that your simplified result wasn't clicking. Yours is so much simpler, but not if it's not how she learned it.

Answer 43

true it's helpful to know how to find the functions, but it's not necessary for this problem. Sometimes it's handy to know how to do something quickly and efficient (eg: if you're trying to make a quick decision on something)

Answer 44

You are ALL uniquely brilliant in your OWN way; I applaud, thank, and appreciate ALL of you for your eagerness to help and dedicated, hard work!!
Genuinely, thank you! :)