Question

已知函数f(x)=2x/(1+x^2),g(x)=(1-x^2)/(1+x^2)求函数f(x)+g(x)的值域

Answer 1

y=f(x)+g(x)=(=2x/(1+x²)+(1-x²)/(1+x²)y=(2x+1-x²)/(1+x²)y=2(x+1)/(1+x²)-1当y=0时x²-2x-1=0(x-1)²=2x=1±√2当x=0时,y=1＞0当x=1时,y=1＞0x＞1+√2,y＜0x＜1-√2,y＜0y...