2f(x)+2f(1-x)=x²,求f(x)解析式

问题描述:

2f(x)+2f(1-x)=x²,求f(x)解析式

2f(x)+f(1-x)=x²用(1-x)替换x2f(1-x)+f[1-(1-x)]=(1-x)²2f(1-x)+f(x)=(1-x)²相加得3f(1-x)+3f(x)=x²+(1-x)²3[f(1-x)+f(x)]=2x²-2x+1f(1-x)+f(x)=(2x²-2x+1)/3f(1-x)+2f(x)=x...