题目内容
已知f (x)是定义在[ 4,4]上的奇函数,在[0,4]单调递增,且,f (x + 1) = f (x) + f (1),设f (x)的反函数是,则= ;f (x)的值域为 .
4, [2,2]
解析:由题设知f (0) = 0,f (4) = 2,f ( 4) = 2,∴,又f (x)在[0,4]递增,∴f (x)在[ 4,4]上递增,∴f (x)的值域为[2,2].
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题目内容
已知f (x)是定义在[ 4,4]上的奇函数,在[0,4]单调递增,且,f (x + 1) = f (x) + f (1),设f (x)的反函数是,则= ;f (x)的值域为 .
4, [2,2]
解析:由题设知f (0) = 0,f (4) = 2,f ( 4) = 2,∴,又f (x)在[0,4]递增,∴f (x)在[ 4,4]上递增,∴f (x)的值域为[2,2].