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Assignment:Find the solution set of inequality arcsin((x+3)*(x+3))-arcsin(x*x) >1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
arcsin ( ( x + 3 ) * ( x + 3 ) ) - arcsin ( x * x ) >1 (1)
From the definition field of arcsin
( x + 3 ) * ( x + 3 ) ≥ -1 (2 )
( x + 3 ) * ( x + 3 ) ≤ 1 (3 )
From the definition field of arcsin
x * x ≥ -1 (4 )
x * x ≤ 1 (5 )
From inequality(1):
The solution set is empty, that is, within the range of real numbers, the inequality will never be established!
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):
-4 ≤ x ≤ -2
From inequality(4):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(5):
-1 ≤ x ≤ 1
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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