pasagot po, salamat po
subject: pre-cal
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pasagot po, salamat posubject: pre-cal
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What are the real values of the variable x that make the expressions defined in the set of real numbers?
1.) 2x + 1
2x + 1 = 0
2x = -1
x = -1/2
2.) √(x² - 1)
√(x² - 1) = 0
(√(x² - 1) = 0)²
x² - 1 = 0
x² = 1
x = 1 ; x = -1
3.) x / (x² - 3x - 4)
x / (x² - 3x - 4) = 0
x = 0
4.) 3x
3x = 0
x = 0
What are the real values of the variable x that make the expressions undefined
1.) 2x + 1
(2x + 1)/0
= undefined
2.) √(x² - 1)
√(x² - 1)/0
undefined
3.) x / (x² - 3x - 4)
x / (4² - 3(4) - 4)
x / 16 - 12 - 4
x / 0
undefined
4.) 3x
3x/0
undefined
What is the domain of the first expression, second, third and fourth expression?
1.) 2x + 1
Domain: (-∞, ∞)
2.) √(x² - 1)
x² - 1 ≥ 0
x² ≥ 0 + 1
x² ≥ 1
±x ≥ 1
-x ≥ 1 ; +x ≥ 1
Domain: x ≤ -1, x ≥ 1
3.) x / (x² - 3x - 4)
x² - 3x - 4
(x - 4)(x + 1)
x - 4 = 0 ; x + 1 = 0
x = 4 ; x = -1
Domain: x ≠ 4, x ≠ -1
4.) 3x
Domain: (-∞, ∞)
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