Question

已知f(x)是奇函数,且f(2-x)=f(x),当x∈[2,3]时,f(x)=log2(x-1),则当x∈[1,2]时,

Answer 1

∵f(x)是奇函数,且f(2-x)=f(x) ∴f(2＋x)＝f(-x)＝﹣f(x)＝﹣f(2－x)＝f(x－2)

∴f(x)＝f(x－4)＝﹣f(4－x)

∵x∈[1,2] ∴4－x∈[2,3] ∴f(4－x)＝㏒2 (3－x)

∴当x∈[1,2]时,f(x)＝﹣㏒2 (3－x)

选 C