Question

Let f : R → Z, where f(x) = 2x − 1.
(a) Find f(A), where A = {x ∈ R | 1 ≤ x ≤ 4}.
(b) Find f ^-1 where B = {−9, −8}.

Answer 1

so you have a line, and you want to know what values are for all xs from 1 to 4,

Answer 2

well all integer values of f(A) that is

Answer 3

one approach is to simply start converting x into f(x)

1 < x < 4

1(2) < 2x < 4(2)

1(2) -1 < 2x-1 < 4(2) -1

Answer 4

do i really just need to plug it in? This is for discrete math. seems way too simple O.o

Answer 5

Its for our part on Set theory, it really didn't occur to me just to plug it in.

Answer 6

the problem is simple just so that you would be able to determine if your solution is correct i spose.

Answer 7

Why explain that Real numbers map onto integers? any reason?

Answer 8

domain (x inputs) are real values

the range f(x) is composed of integers, so its prolly a stepping function

Answer 9

other than that, its just information that you use to determine the required outcome

Answer 10

However, when f is inverted, wouldn't it create some constraint as it makes a fraction for the set of integers? Or I'm just reading to far into it?

Answer 11

\[\{f(A) \in Z~|~1\le f(A)\le7\} \]
or some such stuff

Answer 12

y = 2x-1

(y+1)/2

when y=1,2,3,4,5,6,7

(2,3,4,5,6,7,8)/2 are real values

Answer 13

Assuming Z stands for set of integers, it looks like non integer outputs are undefined.
f(2.3) is therefore undefined, since it is equal to 3.6 which is not an integer

Answer 14

then if memory serves. f does not map real to integer if that is the case

Answer 15

exactly so if I plug in -9 I would get an output of -4, which would be valid but the opposite would occur for -8. And yes, it does stand for set of integers

Answer 16

but f(2.5) is defined

Answer 17

which is why i was thinking of a step function

Answer 18

the domain of the inverse is Z,

Answer 19

Well, by definition ( what I've been taught), A ---> B would mean A means that B is mapped onto A* Im sorry

Answer 20

means that B is mapped onto A *

Answer 21

R to Z is function notation for inputs of R and outputs of Z, not sure why your definition would have it any other way

Answer 22

Well, the books and teacher explanations are different ( maybe?), I mean I don't want to argue about it, that was in the book. By the teacher it said that Z would be the codomain and R would be the domain

Answer 23

granted that the solution set is R,Z is a set if discrete points.