已知偶函数f(X)在区间【0,+∝)单调增加,则满足f(2x-1)<f(1⼀3)的x取值范围是

2025-06-22 22:19:18
推荐回答(2个)
回答1:

case 1:
for
2x-1 >=0
=> x >=1/2
f(2x-1)< f(1/3)
=> 2x-1 < 1/3
x < 2/3
solution for case 1
x >=1/2 and x<2/3
ie 1/2 <= x < 2/3

case 2: x < 1/2
f(2x-1) = f(-(1-2x))) = f(1-2x) < f(1/3)
=> 1-2x < 1/3
=> x > 1/3
solution for case 2
x<1/2 and x> 1/3
ie 1/3< x < 1/2

solution for f(2x-1)case 1 or case 2
1/2 <= x < 2/3 or 1/3< x < 1/2
ie 1/3< x < 2/3

回答2:

2x-1≥0
x≥1/2
2x-1<1/3
x<2/3
1/2≤x<2/3