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Assignment:Find the solution set of inequality lg(acos(x-3))-sqrt(1/x)+(tanx)^0 >-5 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
lg ( arccos ( x - 3 ) ) - sqrt ( 1 / x ) + ( tan x ) ^ 0 > -5 (1)
From the definition field of arccos
x - 3 ≥ -1 (2 )
x - 3 ≤ 1 (3 )
From the definition field of lg
arccos ( x - 3 ) > 0 (4 )
From the definition field of divisor
x ≠ 0 (5 )
From the definition field of √
1 / x ≥ 0 (6 )
From inequality(1):
x > 2
From inequality(2):
x ≥ 2
From inequality(3):
x ≤ 4
From inequality(4):
The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
From inequality(5):
x < 0 或 x > 0
From inequality(6):
x ≥ 0
The final solution set is :
The solution set is empty,that is, the inequality will never be estatlished within the real number range.
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