设函数f(x)=x^2+x-1/4.问:若定义域为[a,a+1]时,f(x)的值域为[-1/2,1/16],求a的值.答案是-4/5或-3/4
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![设函数f(x)=x^2+x-1/4.问:若定义域为[a,a+1]时,f(x)的值域为[-1/2,1/16],求a的值.答案是-4/5或-3/4](/uploads/image/z/1643602-58-2.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx%5E2%2Bx-1%2F4.%E9%97%AE%EF%BC%9A%E8%8B%A5%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%5Ba%2Ca%2B1%5D%E6%97%B6%2Cf%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F%E4%B8%BA%5B-1%2F2%2C1%2F16%5D%2C%E6%B1%82a%E7%9A%84%E5%80%BC.%E7%AD%94%E6%A1%88%E6%98%AF-4%2F5%E6%88%96-3%2F4)
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设函数f(x)=x^2+x-1/4.问:若定义域为[a,a+1]时,f(x)的值域为[-1/2,1/16],求a的值.答案是-4/5或-3/4
设函数f(x)=x^2+x-1/4.问:若定义域为[a,a+1]时,f(x)的值域为[-1/2,1/16],求a的值.
答案是-4/5或-3/4
设函数f(x)=x^2+x-1/4.问:若定义域为[a,a+1]时,f(x)的值域为[-1/2,1/16],求a的值.答案是-4/5或-3/4
考虑到函数的单调性知道,若在[a,a+1]上单调,有f(a)=-1/2;f(a+1)=1/16.或f(a)=1/16;f(a+1)=1/2.不可能.故
f(x)能取得最小值是x=-1/2,说明a
f(x)=(x+1/2)^2-1/2
f(x)能取得最小值是-1/2,说明a<-1/2当a<-1时,f(a)=1/16,解得a=-5/4
当a>=-1时,f(a+1)=1/16,解得a=-3/4