Mapping / Set problem

[Chas3down]

Homework Statement

R = all real numbers

F(x) = { y in R : sin(y) = x}

1. Is F a mapping from R to R

2. Describe the three sets F(5), F(0), F(1).

3.Can F be represtented as a function from R to R

4. Give two different choices of X and Y (take both X and Y to be subsets of ?) so that F can be represented as a function say f X -> Y.

Homework Equations

N/A

The Attempt at a Solution

Just double checking my answers and not sure on last 2.

1. No, it is a mapping from -1 to 1.
2. F(5) = Null set, F(0) = 0 and pi, f(1) = pi/2 and 3pi/2
3. No, the range of the function is only from -1 to 1. ?(Not sure on this one)
4. No clue.

 

[RUber]

For 1) I would be careful on your wording. When you say a mapping from -1 to 1, that is a mapping, M(-1) = 1. Domain = {-1} Range = {1}.
The domain (x values) is on the interval where sin(y)=x is defined for x, and the output range (y values ) are all real numbers, where sin(y) is defined.
For 2) There are more...infinitely more members of F(0) and F(1). Remember, y is in the real numbers.
For 3) what is the definition of a function? Something about one single output for any input.
For 4) You want to use the definition of a function you learned in (3) along with the lessons learned from (2) to define appropriate intervals for X and Y so that F meets the definition of a function.