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General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace for f(x) in the above inequality to find the domain.
The possible solutions of the above inequality are given by the intervals . We need to pick test point from each possible solution interval and check whether that test point make the inequality
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is