f(x)=x^2+(a+2)x+3在[a,b]上为偶函数,求f(b)=?

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f(x)=x^2+(a+2)x+3在[a,b]上为偶函数,求f(b)=?

f(x)=x^2+(a+2)x+3在[a,b]上为偶函数,求f(b)=?
f(x)=x^2+(a+2)x+3在[a,b]上为偶函数,求f(b)=?

f(x)=x^2+(a+2)x+3在[a,b]上为偶函数,求f(b)=?
由“函数f(x)是偶函数的必要条件”可知,a与b是互为相反数,即a+b=0.a<b.且f(x)=f(-x).===>x²+(a+2)x+3=x²-(a+2)x+3.(x∈[a,b])===>a=-2.∴b=2.函数f(x)=x²+3.∴f(b)=f(2)=2²+3=7.