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Assignment:Find the solution set of inequality -1 ≤x-sqrt(1-x) ≤1 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
-1 ≤ x - sqrt ( 1 - x ) (1)
x - sqrt ( 1 - x ) ≤1 (2)
From the definition field of √
1 - x ≥ 0 (3 )
From inequality(1):
x ≥ 0
From inequality(2):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
x ≤ 1
From inequalities (1) and (2)
x ≥ 0 (4)
From inequalities (3) and (4)
0 ≤ x ≤ 1 (5)
The final solution set is :
0 ≤ x ≤ 1Your problem has not been solved here? Please take a look at the hot problems !