函数y=(x²-1)/(x²+1)的值域是?求详解
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函数y=(x²-1)/(x²+1)的值域是?求详解
函数y=(x²-1)/(x²+1)的值域是?求详解
函数y=(x²-1)/(x²+1)的值域是?求详解
y=(x²+1-2)/(x²+1)
=(x²+1)/(x²+1)-2/(x²+1)
=1-2/(x²+1)
x²+1≥1
所以0
y=1-2/(1+x²)
令t=1+x²,则t∈[1,+∞)
y=1-2/t单调递增
t→+∞时,y→1.
所以值域为[-1,1)