函数y=1/(x^2+2x–5)的值域

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函数y=1/(x^2+2x–5)的值域函数y=1/(x^2+2x–5)的值域函数y=1/(x^2+2x–5)的值域数理答疑团为您解答,希望对你有所帮助.y=1/(x^2+2x–5)=1/[(x+1)&

函数y=1/(x^2+2x–5)的值域
函数y=1/(x^2+2x–5)的值域

函数y=1/(x^2+2x–5)的值域
数理答疑团为您解答,希望对你有所帮助.
y=1/(x^2+2x–5) = 1/[(x+1)²-6]
[(x+1)²-6]≥-6,且[(x+1)²-6]≠0;
因此:0>[(x+1)²-6]≥-6或[(x+1)²-6]>0
所以:y≤ -1/6或y>0
函数y=1/(x^2+2x–5)的值域(-∞,-1/6]∪(0,+∞).

因为函数y=1/(x^2+2x–5),所以yx^2+2yx–5y-1=0有解,所以判别式>=0所以y<=-1/6,或y>=0,即函数的值域为(负无穷,-1/6],或[0,正无穷)