设F(x)=(1+2/(2^x -1))×f(x)(x≠0)是偶函数,且f(x)不恒等于0,试判断f(x)是奇函数还是偶函数
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![设F(x)=(1+2/(2^x -1))×f(x)(x≠0)是偶函数,且f(x)不恒等于0,试判断f(x)是奇函数还是偶函数](/uploads/image/z/8928564-60-4.jpg?t=%E8%AE%BEF%28x%29%3D%281%2B2%2F%282%5Ex+-1%29%29%C3%97f%28x%29%28x%E2%89%A00%29%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0%2C%E4%B8%94f%28x%29%E4%B8%8D%E6%81%92%E7%AD%89%E4%BA%8E0%2C%E8%AF%95%E5%88%A4%E6%96%ADf%28x%29%E6%98%AF%E5%A5%87%E5%87%BD%E6%95%B0%E8%BF%98%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0)
设F(x)=(1+2/(2^x -1))×f(x)(x≠0)是偶函数,且f(x)不恒等于0,试判断f(x)是奇函数还是偶函数
设F(x)=(1+2/(2^x -1))×f(x)(x≠0)是偶函数,且f(x)不恒等于0,试判断f(x)是奇函数还是偶函数
设F(x)=(1+2/(2^x -1))×f(x)(x≠0)是偶函数,且f(x)不恒等于0,试判断f(x)是奇函数还是偶函数
F(x)=f(x)(2^x+1)/(2^x-1)
F(-x)=f(-x)(2^(-x)+1)/(2^(-x)-1)=f(-x)(2^x+1)/(1-2^x)=-f(-x)(2^x+1)/(1-2^x)
因为F(x)=F(-x)
f(x)(2^x+1)/(2^x-1)=-f(-x)(2^x+1)/(1-2^x)
f(x)=-f(-x)
f(x)是奇函数
不奇不偶
偶函数