设函数f(x)=|2x-7|+1 .(1) 求不等式f(x)≤|x-1|的解集(2)若存在x使不等式f(x)≤ax成立.求实数a的取值范围.
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![设函数f(x)=|2x-7|+1 .(1) 求不等式f(x)≤|x-1|的解集(2)若存在x使不等式f(x)≤ax成立.求实数a的取值范围.](/uploads/image/z/7302810-66-0.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%7C2x-7%7C%2B1+.%EF%BC%881%EF%BC%89+%E6%B1%82%E4%B8%8D%E7%AD%89%E5%BC%8Ff%28x%29%E2%89%A4%7Cx-1%7C%E7%9A%84%E8%A7%A3%E9%9B%86%EF%BC%882%EF%BC%89%E8%8B%A5%E5%AD%98%E5%9C%A8x%E4%BD%BF%E4%B8%8D%E7%AD%89%E5%BC%8Ff%28x%29%E2%89%A4ax%E6%88%90%E7%AB%8B.%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
设函数f(x)=|2x-7|+1 .(1) 求不等式f(x)≤|x-1|的解集(2)若存在x使不等式f(x)≤ax成立.求实数a的取值范围.
设函数f(x)=|2x-7|+1 .
(1) 求不等式f(x)≤|x-1|的解集
(2)若存在x使不等式f(x)≤ax成立.求实数a的取值范围.
设函数f(x)=|2x-7|+1 .(1) 求不等式f(x)≤|x-1|的解集(2)若存在x使不等式f(x)≤ax成立.求实数a的取值范围.
(1)分别令2x-7=0和x-1=0,分别得x=7/2与x=1,以此两点对x分段,分类讨论,去绝对值.最后得3
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(1) |2x-7|+1≤|x-1|
(2x-7)+1≤x-1
x≤5
(2x-7)+1 ≤-(x-1)
2x-6≤-x+1
3x≤7
x≤7/3
-(2x-7)+1 ≤(x-1)
-...
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(1) |2x-7|+1≤|x-1|
(2x-7)+1≤x-1
x≤5
(2x-7)+1 ≤-(x-1)
2x-6≤-x+1
3x≤7
x≤7/3
-(2x-7)+1 ≤(x-1)
-2x+9.≤x-1
-3x≤-10
x≥10/3
-(2x-7)+1 ≤-(x-1)
-2x+9.≤-x+1
-2x≤-8
x≥4
(2)|2x-7|+1 ≤ax
(2x-7)+1 ≤ax或-(2x-7)+1 ≤ax
( 2-a)x ≤ 6 ( -2-a )x ≤6 .
a ≤2 a ≤-2
收起
(1)x的范围为:[7/3,5]
(2)a的范围为:a>=2或a<=-2