عين المجال والمدى للدالة srqt(x/(x² - 1)) ..l
الأربعاء، 21 مارس 2012
التسميات:
الجبر
f(x) = sqrt[x/(x² - 1)]
x² - 1 = 0 x = ±1
x/(x² - 1) ≥ 0
the domain in ]-1 , 0] ∪ ]1 , ∞[
..............................................
y = sqrt[x/(x² - 1)]
y² = x/(x² - 1)
x = y²(x² - 1)
x = x²y² - y²
y²x² - x - y² = 0
Delta = 1 + 4y^4
x = [1 ± sqrt(1+4y^4)]/2y²
the co-domain IR - {0}
but the negative numbers switch the function
to ±y = sqrt[x/(x² - 1)]
so we take the positive case
Hence : the rang is [0 , ∞[
x² - 1 = 0 x = ±1
x/(x² - 1) ≥ 0
the domain in ]-1 , 0] ∪ ]1 , ∞[
..............................................
y = sqrt[x/(x² - 1)]
y² = x/(x² - 1)
x = y²(x² - 1)
x = x²y² - y²
y²x² - x - y² = 0
Delta = 1 + 4y^4
x = [1 ± sqrt(1+4y^4)]/2y²
the co-domain IR - {0}
but the negative numbers switch the function
to ±y = sqrt[x/(x² - 1)]
so we take the positive case
Hence : the rang is [0 , ∞[
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