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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)=?
题目详情
f（x）=x+1/x-1(x不等于正负1)则f(x)乘f(-x)=?f(-x)+f(x)=?
▼优质解答
答案和解析
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
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
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