mathdad
Full Member
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- Apr 24, 2015
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Find domain of sqrt{x - 3x^2}.
I will begin by setting the radicand to be greater than or equal to 0.
x - 3x^2 ≥ 0
x(1 - 3x) ≥ 0
x ≥ 0 and 1 - 3x ≥ 0 leads to
- 3x ≥ -1.
x ≤0 1/3
Set on number line.
<-------0----------(1/3)------------>
Select a number from each region (including 0 and 1/3) to test x - 3x^2 ≥ 0.
When x = -1, x - 3x^2 ≥ 0 becomes a false statement.
When x = 0, x - 3x^2 ≥ 0 is a true statement. We include 0.
When x = 1, x - 3x^2 ≥ 0 becomes a false statement.
When x = 1/3, x - 3x^2 ≥ 0 is a true statement. We include 1/3.
When x = 2, x - 3x^2 ≥ 0 becomes a false statement.
Domain: {x| 0 ≤ x ≤ 1/3} or [0, 1/3].
Correct?
I will begin by setting the radicand to be greater than or equal to 0.
x - 3x^2 ≥ 0
x(1 - 3x) ≥ 0
x ≥ 0 and 1 - 3x ≥ 0 leads to
- 3x ≥ -1.
x ≤0 1/3
Set on number line.
<-------0----------(1/3)------------>
Select a number from each region (including 0 and 1/3) to test x - 3x^2 ≥ 0.
When x = -1, x - 3x^2 ≥ 0 becomes a false statement.
When x = 0, x - 3x^2 ≥ 0 is a true statement. We include 0.
When x = 1, x - 3x^2 ≥ 0 becomes a false statement.
When x = 1/3, x - 3x^2 ≥ 0 is a true statement. We include 1/3.
When x = 2, x - 3x^2 ≥ 0 becomes a false statement.
Domain: {x| 0 ≤ x ≤ 1/3} or [0, 1/3].
Correct?
