急,设函数f(x)=x²-x-+1\2的定义域为[n,n+1],n∈正整数,求f(x)的值域中所含的整数的个数f(x)=x²-x+1\2
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![急,设函数f(x)=x²-x-+1\2的定义域为[n,n+1],n∈正整数,求f(x)的值域中所含的整数的个数f(x)=x²-x+1\2](/uploads/image/z/5923457-17-7.jpg?t=%E6%80%A5%2C%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx%26sup2%3B-x-%2B1%5C2%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%5Bn%2Cn%2B1%5D%2Cn%E2%88%88%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E6%B1%82f%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F%E4%B8%AD%E6%89%80%E5%90%AB%E7%9A%84%E6%95%B4%E6%95%B0%E7%9A%84%E4%B8%AA%E6%95%B0f%28x%29%3Dx%26sup2%3B-x%2B1%5C2)
急,设函数f(x)=x²-x-+1\2的定义域为[n,n+1],n∈正整数,求f(x)的值域中所含的整数的个数f(x)=x²-x+1\2
急,设函数f(x)=x²-x-+1\2的定义域为[n,n+1],n∈正整数,求f(x)的值域中所含的整数的个数
f(x)=x²-x+1\2
急,设函数f(x)=x²-x-+1\2的定义域为[n,n+1],n∈正整数,求f(x)的值域中所含的整数的个数f(x)=x²-x+1\2
f(x)=x^2-x+(1/2)=(x-(1/2))^2+(1/4)
对称轴为x=1/2
而:n∈正整数
所以:在[n,n+1]单调递增
f(n)=n^2-n+(1/2),最小整数值=n^2-n+1
f(n+1)=(n+1)^2-(n+1)+(1/2),最大整数值=(n+1)^2-(n+1)=n^2+n
整数的个数=(n^2+n)-(n^2-n+1)+1=2n
f(x)=x²-x-+1\2写错了吧!