y=5x/(x*x-3x+2)+arcsin1/x的定义域
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y=5x/(x*x-3x+2)+arcsin1/x的定义域
y=5x/(x*x-3x+2)+arcsin1/x的定义域
y=5x/(x*x-3x+2)+arcsin1/x的定义域
定义域:x²-3x+2≠0 【分母不为0】
-1≤1/x≤1 【根据arcsinx中的|x|≤1】
即(x-1)(x-2)≠0
x≥1或x≤-1
解得x∈(-∞,-1]∪(1,2)∪(2,+∞)
答案:x∈(-∞,-1]∪(1,2)∪(2,+∞)
祝学习快乐
x²-3x+2≠0,且-1≤1/x≤1
(x-1)(x-2)≠0,那么x≠1,且x≠2
-1≤1/x≤1,1+1/x≥0,且1/x-1≤0,即(x+1)/x≥0,且(x-1)/x≥0,解得:x≥1,或x≤-1
所以x>1,或x≤-1,且x≠2
即定义域为(-∞,-1]∪(1,2)∪(2,+∞)
x≠0,1,2
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