数学函数计算已知函数f(x)=x²/1+x²求f(2)+f(1/2),f(3)+f(1/3)求证:f(x)+f(1/x)是定值计算f(1)+f(2)+f(1/2)+f(1/3)+f(4)+f(1/4)的值
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![数学函数计算已知函数f(x)=x²/1+x²求f(2)+f(1/2),f(3)+f(1/3)求证:f(x)+f(1/x)是定值计算f(1)+f(2)+f(1/2)+f(1/3)+f(4)+f(1/4)的值](/uploads/image/z/9978900-60-0.jpg?t=%E6%95%B0%E5%AD%A6%E5%87%BD%E6%95%B0%E8%AE%A1%E7%AE%97%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dx%26%23178%3B%2F1%2Bx%26%23178%3B%E6%B1%82f%EF%BC%882%EF%BC%89%2Bf%EF%BC%881%2F2%EF%BC%89%2Cf%EF%BC%883%EF%BC%89%2Bf%EF%BC%881%2F3%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9Af%EF%BC%88x%EF%BC%89%2Bf%EF%BC%881%2Fx%EF%BC%89%E6%98%AF%E5%AE%9A%E5%80%BC%E8%AE%A1%E7%AE%97f%EF%BC%881%EF%BC%89%2Bf%EF%BC%882%EF%BC%89%2Bf%EF%BC%881%2F2%EF%BC%89%2Bf%EF%BC%881%2F3%EF%BC%89%2Bf%EF%BC%884%EF%BC%89%2Bf%281%2F4%29%E7%9A%84%E5%80%BC)
数学函数计算已知函数f(x)=x²/1+x²求f(2)+f(1/2),f(3)+f(1/3)求证:f(x)+f(1/x)是定值计算f(1)+f(2)+f(1/2)+f(1/3)+f(4)+f(1/4)的值
数学函数计算
已知函数f(x)=x²/1+x²
求f(2)+f(1/2),f(3)+f(1/3)
求证:f(x)+f(1/x)是定值
计算f(1)+f(2)+f(1/2)+f(1/3)+f(4)+f(1/4)的值
数学函数计算已知函数f(x)=x²/1+x²求f(2)+f(1/2),f(3)+f(1/3)求证:f(x)+f(1/x)是定值计算f(1)+f(2)+f(1/2)+f(1/3)+f(4)+f(1/4)的值
f(1/x)=1/(1+x²)]
f(x)=x²/1+x²=1-[1/(1+x²)]=1-f(1/x)
f(x)+f(1/x)=1
所以f(2)+f(1/2)=1
f(3)+f(1/3)=1
2)由1)得,f(x)+f(1/x)=1
3)f(1)+f(2)+f(1/2)+f(1/3)+f(4)+f(1/4)
=f(1)+[f(2)+f(1/2)]+[f(4)+f(1/4)]+f(1/3)
=f(1)+(1)+(1)+f(1/3)
=2+f(1)+[1-f(3)]
=3+f(1-f(3)]
=3+(1/2)-9/10
=2.6