已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?(2)证明f(x)是偶函数.请解答者列出一定的过程,
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![已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?(2)证明f(x)是偶函数.请解答者列出一定的过程,](/uploads/image/z/14870573-53-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3f%28x%2By%29%2Bf%28x-y%29%3D2f%28x%29%C3%97f%28y%29.%28x%E2%88%88R%2Cy%E2%88%88R.%29%2C%E4%B8%94f%280%29%E2%89%A00.%281%29%E6%B1%82f%280%29%3D%3F%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%E6%BB%A1%E8%B6%B3f%28x%2By%29%2Bf%28x-y%29%3D2f%28x%29%C3%97f%28y%29.%28x%E2%88%88R%2Cy%E2%88%88R.%29%2C%E4%B8%94f%280%29%E2%89%A00.%281%29%E6%B1%82f%280%29%3D%3F%282%29%E8%AF%81%E6%98%8Ef%28x%29%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0.%E8%AF%B7%E8%A7%A3%E7%AD%94%E8%80%85%E5%88%97%E5%87%BA%E4%B8%80%E5%AE%9A%E7%9A%84%E8%BF%87%E7%A8%8B%2C)
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?(2)证明f(x)是偶函数.请解答者列出一定的过程,
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?(2)证明f(x)是偶函数.请解答者列出一定的过程,
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y).(x∈R,y∈R.),且f(0)≠0.(1)求f(0)=?(2)证明f(x)是偶函数.请解答者列出一定的过程,
(1)因为f(x+y)+f(x-y)=2f(x)×f(y),所以f(0+0)+f(0-0)=2f(0)×f(0),又因为f(0)≠0 所以有f(0)=1; (2)f(-x)+f(x)=f(-x+0)+f(x+0)=2f(x)f(0)=2f(x),所以有f(-x)=f(x)从而f(x)为偶函数.
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