[MOVED] Domain of the function x-1/2x-3
- Thread starter Jade
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Probably not, but it's hard to say. How did you come to that conclusion?Jade said:
When you reply with your work and reasoning, please also clarify the function. What you have posted could mean any of the following:
. . . . .f(x) = x - 1/(2x) - 3
. . . . .g(x) = x - 1/(2x - 3)
. . . . .h(x) = x - (1/2)x - 3
. . . . .j(x) = (x - 1)/(2x) - 3
. . . . .k(x) = (x - 1)/(2x - 3)
There may be other interpretations....
Eliz.
It is a broad Domain question
The question is listed: Find the domain of each function. The one I have the problem with is x-1/2x+3.
They are asking what numbers can fit into that to make it true. I am thinking any real numbers?!
Another one was "sqrt" 4-3x. My answer was [4/3, infinity) because any square root has to be greater than or equal to zero. I am thinking in a fraction it can be really any number?? Am I on track here?[/list]
The question is listed: Find the domain of each function. The one I have the problem with is x-1/2x+3.
They are asking what numbers can fit into that to make it true. I am thinking any real numbers?!
Another one was "sqrt" 4-3x. My answer was [4/3, infinity) because any square root has to be greater than or equal to zero. I am thinking in a fraction it can be really any number?? Am I on track here?[/list]
- Joined
- Feb 4, 2004
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- 16,582
Yes, and as pointed out earlier, there are many different interpretations of "x-1/2x+3".Jade said:
If you mean sqrt[4] - 3x, the domain will be one thing. If you mean sqrt[4 - 3x], the domain will be another thing. If you mean fourth-root[-3x], the domain will be yet another thing. If you mean something else, the domain might be something else. Since your formatting is unclear, we have no way of knowing what the answer should be.Jade said:
Since the domain of a function will depend upon what that function actually is, please reply with the requested clarifications.
Thank you.
Eliz.
Re: It is a broad Domain question
Please re-read Stapel's response. There are many possible interpretations for the way you have typed your problem; we can't give you specific help without knowing exactly which interpretation fits the problem.
Here's a "broad domain answer":
If the variable appears in the denominator of a fraction, any value of the variable which makes that denominator become 0 must be eliminated from the domain.
If the variable appears under a radical sign with an EVEN index (like square root, fourth root, 6th root, etc.) then what is under the radical sign must be non-negative. You appear to have some understanding of this....but, the answer given for your example is incorrect. If you have sqrt(4 - 3x), then (4 - 3x) must be greater than or equal to 0:
4 - 3x > 0
-3x > -4
Divide both sides by -3; remember that when you divide both sides of an inequality by a negative number, you must switch the direction of the inequality symbol:
(-3x) / (-3) < (-4)/(-3)
x < 4/3
So, the domain is (-infinity, 4/3]
I hope this helps you.
Jade said:
Please re-read Stapel's response. There are many possible interpretations for the way you have typed your problem; we can't give you specific help without knowing exactly which interpretation fits the problem.
Here's a "broad domain answer":
If the variable appears in the denominator of a fraction, any value of the variable which makes that denominator become 0 must be eliminated from the domain.
If the variable appears under a radical sign with an EVEN index (like square root, fourth root, 6th root, etc.) then what is under the radical sign must be non-negative. You appear to have some understanding of this....but, the answer given for your example is incorrect. If you have sqrt(4 - 3x), then (4 - 3x) must be greater than or equal to 0:
4 - 3x > 0
-3x > -4
Divide both sides by -3; remember that when you divide both sides of an inequality by a negative number, you must switch the direction of the inequality symbol:
(-3x) / (-3) < (-4)/(-3)
x < 4/3
So, the domain is (-infinity, 4/3]
I hope this helps you.