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The process and results of the four major problems in compulsory mathematics
(1) When a= 1

f(x)=√2sin(x-π/4)+b

π/2+2kπ& lt; = x-π/4 & lt; =3π/2+2kπ,k∈Z

π/4+2kπ& lt; = x & lt=5π/4+2kπ,k∈Z

∴ Monotone decreasing interval [π/4+2kπ, 5π/4+2kπ], k∈Z

(2)

∫x∈[0,π]

∴x-π/4∈[-π/4,3π/4]

∴sin(x-π/4)∈[-√2/2, 1]

A & lt0

∴√2asin(x-π/4)∈[√2a,-a]

∴f(x)∈[√2a+a+b,b]

* The range is [2,3]

∴b=3

√2a+a+b=2

a =- 1/( 1+√2)= 1-√2。

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