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[ 1/1Inequality]
Assignment:Find the solution set of inequality -1 ≤(3y-1)/(1+y^2)^0.5 ≤1 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
-1 ≤ ( 3 * y - 1 ) / ( 1 + y ^ 2 ) ^ 0.5 (1)
( 3 * y - 1 ) / ( 1 + y ^ 2 ) ^ 0.5 ≤1 (2)
From the definition field of divisor
1 + x ^ 2 ≠ 0 (3 )
From inequality(1):
y ≥ 0
From inequality(2):
y ≤ 3/4
From inequality(3):
y ∈ R (R为全体实数),即在实数范围内,不等式恒成立!
From inequalities (1) and (2)
0 ≤ y ≤ 3/4 (4)
From inequalities (3) and (4)
0 ≤ y ≤ 3/4 (5)
The final solution set is :
0 ≤ y ≤ 3/4Your problem has not been solved here? Please take a look at the hot problems !