缺少等號設(shè)f(x)=ax5+bsinx+x2,且f(-2)=3,則f(2)=_________.
解:令g(x)=f(x)-x2=ax5+bsinx
由函數(shù)奇偶性的性質(zhì)可知g(x)為奇函數(shù)
∵f(-2)=3
∴g(-2)=f(-2)-4=-1
∴g(2)=1
∴f(2)=g(2)+4=5
故答案為:5
分析:函數(shù)f(x)是非奇非偶函數(shù),但由函數(shù)奇偶性的性質(zhì)可知:f(x)-x2=ax5+bsinx為奇函數(shù),故可構(gòu)造此函數(shù)進行求解.
點評:本題考查的知識點為奇函數(shù)及函數(shù)的值,其中構(gòu)造函數(shù)f(x)-x2=ax5+bsinx,然后將問題轉(zhuǎn)化為利用奇函數(shù)的定義求值,是解答本題的關(guān)鍵.