L R.
asked • 08/29/15Find the domain of the expression in interval notation
(√7x) /x+7
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1 Expert Answer
Christopher G. answered • 08/29/15
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Math, Science, Test Prep
Assuming the assumptions I made in the comment above are correct, then there are two conditions that could affect the domain for this expression:
1) √(7x) will only exist if the inside of the radical is non-negative. Therefore we can conclude that:
1) √(7x) will only exist if the inside of the radical is non-negative. Therefore we can conclude that:
7x ≥ 0
x ≥ 0
2) Secondly, the expression will not exist if the denominator equals zero. This implies that:
x + 7 ≠ 0
x ≠ -7
This second condition is actually irrelevant, because we already knew from the first condition that x had to be ≥ 0. Therefore, the domain is simply:
x ≥ 0
In interval notation this could be written:
[0, ∞)
L R.
Yes, i meant the latter one you proposed. I'm still confused as to why it's o instead of -7. Because, wouldn't be -7 due to the fact that it makes the denominator 0?
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08/29/15
Christopher G.
Forgive the lateness of this response, as I was just watching Michael Clayton starring George Clooney. You are correct that x = -7 is prohibited because of the second condition. However, since all negative numbers were already prohibited by the first condition, this is redundant.
If that is not clear, consider the following number lines. To be part of the domain, a number must satisfy both conditions 1) and 2). The only points that satisfy both conditions are those that are shaded in each of the following number lines, namely those points that are ≥ 0.
Condition 1) <??O??????????>
-7
Condition 2) <--------------???????>
0
If that is not clear, consider the following number lines. To be part of the domain, a number must satisfy both conditions 1) and 2). The only points that satisfy both conditions are those that are shaded in each of the following number lines, namely those points that are ≥ 0.
Condition 1) <??O??????????>
-7
Condition 2) <--------------???????>
0
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08/30/15
Christopher G.
Oops, it looks like my Unicode characters didn't render the way I wanted them to, so let me try those number lines again:
Condition 1) <===◊============>
-7
Condition 2) <---------------♦=======>
0
Condition 1) <===◊============>
-7
Condition 2) <---------------♦=======>
0
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08/30/15
L R.
Thank you so much Christopher you have been of great help.
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09/04/15
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Michael J.
08/29/15