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Assignment:Find the solution set of inequality ex ≥x+1 ≥lnx+2 .
Question type: Inequality
Solution:
The inequality can be reduced to 2 inequalities:
e x ≥ x + 1 (1)
x + 1 ≥ ln x + 2 (2)
From the definition field of ln
x > 0 (3 )
From inequality(1):
x ≤ 0 或 0 ≤ x ≤ 0 或 x ≥ 0
From inequality(2):
x ≤ 1 或 1 ≤ x ≤ 1 或 x ≥ 1
From inequality(3):
x > 0
From inequalities (1) and (2)
x ≤ 0 或 0 ≤ x ≤ 0 或 0 ≤ x ≤ 1 或 1 ≤ x ≤ 1 或 x ≥ 1 (4)
From inequalities (3) and (4)
0 < x ≤ 0 或 0 ≤ x ≤ 0 或 0 ≤ x ≤ 1 或 1 ≤ x ≤ 1 或 x ≥ 1 (5)
The final solution set is :
0 < x ≤ 0 或 0 ≤ x ≤ 0 或 0 ≤ x ≤ 1 或 1 ≤ x ≤ 1 或 x ≥ 1Your problem has not been solved here? Please take a look at the hot problems !