Answer:
Let us say the domain in the first case, has the numbers. And the co-domain has the students, .
Now for a relation to be a function, the input should have exactly one output, which is true in this case because each number is associated (picked up by) with only one student.
The second condition is that no element in the domain should be left without an output. This is taken care by the equal number of students and the cards. 25 cards and 25 students. And they pick exactly one card. So all the cards get picked.
Note that this function is one-one and onto in the sense that each input has different outputs and no element in the co domain is left without an image in the domain. Since this is an one-one onto function inverse should exist. If the inverse exists, then the domain and co domain can be interchanged. i.e., Students become the domain and the cards co-domain, exactly like Mario claimed. So, both are correct!
Plug x = 0 into the function
f(x) = x^3 + 2x - 1
f(0) = 0^3 + 2(0) - 1
f(0) = -1
Note how the result is negative. The actual number itself doesn't matter. All we care about is the sign of the result.
Repeat for x = 1
f(x) = x^3 + 2x - 1
f(1) = 1^3 + 2(1) - 1
f(1) = 2
This result is positive.
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We found that f(0) = -1 and f(1) = 2. The first output -1 is negative while the second output 2 is positive. Going from negative to positive means that, at some point, we will hit y = 0. We might have multiple instances of this happening, or just one. We don't know for sure. The only thing we do know is that there is at least one root in this interval.
To actually find this root, you'll need to use a graphing calculator because the root is some complicated decimal value. Using a graphing calculator, you should find the root to be approximately 0.4533976515
1lbs is 16oz, so do the math: 16x3 is 48. 3lbs is 48oz, meaning this is false.
