Question

Someone help

http://i60.tinypic.com/s1831u.png

Answer 1

dont we tend to find f(x) first, then solve for delta?

Answer 2

|f(x)-a| < b

0 < f(x)-a < b

a < f(x) < b-a

Answer 3

b+a that is ... but typos persist

Answer 4

I'm so confused I have no idea what to do or what variable is what

Answer 5

you are simply finding a value which fits the information. you have to have some idea as to what is going on tho.

the basic process is to determine the interval of f(x) which fits and determine the the \(\delta\) from it.

Answer 6

since all you have is a line for f(x), this should amount to a pretty simple process.

Answer 7

given:

|f(x)-3| > 2

solve for the interval of f(x)

Answer 8

<2 tha tis

Answer 9

so since f(x)=3 is would be |3-3|<2?

Answer 10

lets work thru it

|f(x) - 3| < 2

another way to write this is by saying the the value of f(x)-3 is: (-2,-1,0,1,2) or simply

-2 < f(x)-3 < 2 , adding off the 3 we get

-2+3 < f(x) < 2+3

good so far?

Answer 11

Yes I am

Answer 12

now we take this range and use the graph to convert it into a domain

a range of: 1 < f(x) < 5 converts to a domain of: 1 < x < 3

right?

Answer 13

Yes that's what I got when I graphed it!

Answer 14

now, since this is a line, the process is greatly simplified. we want to find x-2, not x so subtract 2 from it all

1-2 < x-2 < 3-2

-1 < x-2 < 1

or written another way:\[|x-2|<1\]

Answer 15

so then the answer for the first is 1? and then I just do the same thing for the second part?

Answer 16

correct

Answer 17

if we had been given a curve, then the interval of our domain might not have been so even on both sides:

say we had gotten something like: -4 < x-2 < 3

the value of delta would be the smaller of the endpoints ... delta=3

Answer 18

okay thank you :D

Answer 19

youre welcome