f(x)=x+1/x-1(x不等于正负1)则f(x)乘f(-x)=?f(-x)+f(x)=?
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![f(x)=x+1/x-1(x不等于正负1)则f(x)乘f(-x)=?f(-x)+f(x)=?](/uploads/image/z/14540466-66-6.jpg?t=f%EF%BC%88x%EF%BC%89%3Dx%2B1%2Fx-1%28x%E4%B8%8D%E7%AD%89%E4%BA%8E%E6%AD%A3%E8%B4%9F1%29%E5%88%99f%28x%29%E4%B9%98f%28-x%29%3D%3Ff%28-x%29%2Bf%28x%29%3D%3F)
f(x)=x+1/x-1(x不等于正负1)则f(x)乘f(-x)=?f(-x)+f(x)=?
f(x)=x+1/x-1(x不等于正负1)则f(x)乘f(-x)=?f(-x)+f(x)=?
f(x)=x+1/x-1(x不等于正负1)则f(x)乘f(-x)=?f(-x)+f(x)=?
f(x)=(x 1)/(x-1)
f(-x)=(-x 1)/(-x-1)=(x-1)/(x 1)
f(x)乘f(-x) = [(x 1)/(x-1)]X[(x-1)/(x 1)] = 1
f(x)加f(-x) = [(x 1)/(x-1)] [(x-1)/(x 1)]
让分母一样,
(x 1)x(x-1) = (x^2)-1
[(x 1)/(x-1)] [(x-1)/(x 1)] = [(x^2)-1 (x^2)-1]/[(x^2)-1] = [2〔(x^2)-1〕]/[(x^2)-1] = 2
结论,
f(x)乘f(-x) = 1
f(x)加f(-x) = 2