Why Are 0 and 4 Excluded from the Range in This Function?

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The discussion centers on the exclusion of 0 and 4 from the range of a function, with the initial answer suggesting the range should be 0 ≤ x ≤ 4. However, the correct range is stated as 0 < x < 4, prompting questions about the reasoning behind this exclusion. One participant argues that since the domain includes 6, which leads to a calculation of 4, both endpoints should be included. Ultimately, it is clarified that 0 and 4 are indeed part of the range, despite the initial confusion. This highlights the importance of understanding the definitions of open and closed intervals in mathematical functions.
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Homework Statement


Please refer to the image attached. The first part, (i).

Homework Equations


None.

The Attempt at a Solution



My answer is 0 </= x </= 4, but the answer says 0<x<4.
Why are 0 and 4 not included?

Since the domain includes 6, then 0.5(6)+1 =4, 4 should be included right?
 

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coconut62 said:

Homework Statement


Please refer to the image attached. The first part, (i).

Homework Equations


None.


The Attempt at a Solution



My answer is 0 </= x </= 4, but the answer says 0<x<4.
Why are 0 and 4 not included?

Since the domain includes 6, then 0.5(6)+1 =4, 4 should be included right?

You are right,0 and 4 are part of the range.
 
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