已知f(x)为反比例函数,且f(x+1)+f(2x+1)=4x²+5x,求f(x)
问题描述:
已知f(x)为反比例函数,且f(x+1)+f(2x+1)=4x²+5x,求f(x)
答
f(x)为反比例函数
f(x)=k/x
f(x+1)+f(2x+1)=4x²+5x
k/(x+1)+k/(2x+1)=4x²+5x
k((x+1)+(2x+1))/(x+1)(2x+1)=4x²+5x
k(3x+2)/(x+1)(2x+1)=4x²+5x
k=(x+1)(2x+1)(4x²+5x)/3x+2
f(x)=(x+1)(2x+1)(4x²+5x)/(3x+2)x
f(x)=(x+1)(2x+1)(4x+5)/(3x+2)