Domain & Range of f: 0 ≤ x ≤ 6, 0 < f(x) < 4

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The discussion centers on the domain and range of the function defined by 0 ≤ x ≤ 6 and 0 < f(x) < 4. Participants debate why the range excludes the endpoints, specifically why f(x) cannot equal 0 or 4. The consensus is that while x can take values of 0 and 6, the function f(x) must remain strictly between 0 and 4, hence the notation 0 < f(x) < 4. This distinction is crucial for understanding the behavior of the function at its boundaries. The clarification emphasizes the importance of strict inequalities in defining the range of the function.
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The question is from http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w10_qp_13.pdf

question no. 7 (i). I think it should be more than easy for a functions fanatic( or someone who does math regularly for that matter) to get the right answer, but as one can clearly see I can't.
The answer says 0 < f(x) < 4. But I am getting 0 ≤ f(x) ≤ 4. Why are 0 and 4 not inclusive?
Because it clearly says in the question X CAN take up 0 and 6, for which the corresponding Y value should be 0 and 4 respectively.
 
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hi mutineer123! :wink:
mutineer123 said:
The answer says 0 < f(x) < 4. But I am getting 0 ≤ f(x) ≤ 4. Why are 0 and 4 not inclusive?
Because it clearly says in the question X CAN take up 0 and 6, for which the corresponding Y value should be 0 and 4 respectively.

your answer looks right to me :smile:
 

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