عين المجال والمدى للدالة srqt(x/(x² - 1)) ..l

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 , ∞[‏‏