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

In summary, The question asks why the answer for 0 < f(x) < 4 is not inclusive, when the question states that x can take on the values of 0 and 6 with corresponding y values of 0 and 4 respectively. The person asking the question believes their answer of 0 ≤ f(x) ≤ 4 is correct.
  • #1
mutineer123
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0
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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  • #2
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:
 

What is the domain of the function f?

The domain of the function f is the set of all possible input values or x-values. In this case, the domain is restricted to values between 0 and 6, inclusive.

What is the range of the function f?

The range of the function f is the set of all possible output values or y-values. In this case, the range is restricted to values between 0 and 4, but not including 0.

Can the function f have an output of 0?

No, the function f cannot have an output of 0 because the range is restricted to values greater than 0.

What does the notation 0 ≤ x ≤ 6 mean?

The notation 0 ≤ x ≤ 6 means that the values of x must be greater than or equal to 0 and less than or equal to 6. In other words, the domain is restricted to values between 0 and 6, including both endpoints.

What does the notation 0 < f(x) < 4 mean?

The notation 0 < f(x) < 4 means that the values of f(x) must be greater than 0 and less than 4. In other words, the range is restricted to values between 0 and 4, but not including 0.

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