已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/21 17:18:40
![已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值](/uploads/image/z/7015407-15-7.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%E4%B9%98f%28y%29%2C%E4%B8%94f%280%29%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E8%8B%A5f%28%CF%80%2F2%29%3D0%2C%E6%B1%82f%28%CF%80%29%E5%8F%8Af%282%CF%80%29%E7%9A%84%E5%80%BC)
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)乘f(y),且f(0)不等于0,若f(π/2)=0,求f(π)及f(2π)的值
令y=0则2f(x)= 2f(x)f(0) 所以f(0)= 1,然后令x=π/2,y=π/2,所以f(π)+f(0)=2f(π/2)f(π/2)=0,所以f(π)=-1,然后令x=y=π,则f(2π)+f(0)=2f(π)f(π),所以f(2π)=1
已知函数f(x)对于任意实数xy 满足f(x+y)=f(x)+f(y).求证f(x-y)=f(x)-f(y)
已知函数f(x)满足f(x+y)+f(x-y)=2f(x)×f(y),且f(0)≠0,证明f(x)是偶函数
已知函数y=f(X)满足f(x)=2f(1/x)+x,求f(x)的表达式
已知函数y=f(x)满足3f(x)+f(-x)=5x,则f(x)=
已知二次函数y=f(x)满足f(x+1)=f(x)+x+1,求f(x)
已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y),则f(2015)=
已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y).则f(2010)
已知函数f(x)满足,f(1)=0.25,4f(x)f(y)=f(x+y)+f(x-y) 则f(2010)=
已知函数f(x)满足f(2)=1/2,2f(x)f(y)=f(x+y)+f(x-y),则f(2012)=?
已知函数f(x)满足f(1)=1/4,f(x)+f(y)=4f(x+y/2)*f(x-y/2)则f(-2011)=?
已知函数f(x)满足f(3)=1/3,3f(x)f(y)=f(x+y)+f(x-y),求f(1812)
已知函数f(x)满足:f(1)=0,f(x)f(y)=f(x+y)+f(x-y),则f(2014)=
高中数学函数题已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y) (x,y属于R),则f(2010)=?已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y) (x,y属于R),则f(2010)=?
已知函数y=f(x)满足f(-2)>f(-1),f(-1)
已知函数f(x)满足f(x)+3f(-x)=3x,求f(x)
已知函数f(x)满足f(ab)=f(a)+f(b),求证:f(x/y)=f(x)-f(y)(y≠0).
已知函数f(x)满足:f(1)=1/4,4f(x)f(y)=f(x+y)+f(x-y).则f(2010)=?(x,y属于R)为什么f(x+3)=-f(x+6)
已知一次函数f(x)满足f[f(x)]=4x+3,求f(x)