若非零函数F(X)对任意实数a,b均有F(a+b)=f(a)*f(b),且x小于0时,f(x)大于1;(1)求证:f(x)大于0(2)求证:(x)为减函数(3)当F(4)=1/16时,解不等式F(X-3)*F(5-X^2)小于等于1/4
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![若非零函数F(X)对任意实数a,b均有F(a+b)=f(a)*f(b),且x小于0时,f(x)大于1;(1)求证:f(x)大于0(2)求证:(x)为减函数(3)当F(4)=1/16时,解不等式F(X-3)*F(5-X^2)小于等于1/4](/uploads/image/z/2690536-40-6.jpg?t=%E8%8B%A5%E9%9D%9E%E9%9B%B6%E5%87%BD%E6%95%B0F%28X%29%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0a%2Cb%E5%9D%87%E6%9C%89F%28a%2Bb%29%3Df%28a%29%2Af%28b%29%2C%E4%B8%94x%E5%B0%8F%E4%BA%8E0%E6%97%B6%2Cf%28x%29%E5%A4%A7%E4%BA%8E1%3B%281%29%E6%B1%82%E8%AF%81%3Af%28x%29%E5%A4%A7%E4%BA%8E0%282%29%E6%B1%82%E8%AF%81%3A%28x%29%E4%B8%BA%E5%87%8F%E5%87%BD%E6%95%B0%283%29%E5%BD%93F%284%29%3D1%2F16%E6%97%B6%2C%E8%A7%A3%E4%B8%8D%E7%AD%89%E5%BC%8FF%28X-3%29%2AF%285-X%5E2%29%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%BA%8E1%2F4)
若非零函数F(X)对任意实数a,b均有F(a+b)=f(a)*f(b),且x小于0时,f(x)大于1;(1)求证:f(x)大于0(2)求证:(x)为减函数(3)当F(4)=1/16时,解不等式F(X-3)*F(5-X^2)小于等于1/4
若非零函数F(X)对任意实数a,b均有F(a+b)=f(a)*f(b),且x小于0时,f(x)大于1;
(1)求证:f(x)大于0
(2)求证:(x)为减函数
(3)当F(4)=1/16时,解不等式F(X-3)*F(5-X^2)小于等于1/4
若非零函数F(X)对任意实数a,b均有F(a+b)=f(a)*f(b),且x小于0时,f(x)大于1;(1)求证:f(x)大于0(2)求证:(x)为减函数(3)当F(4)=1/16时,解不等式F(X-3)*F(5-X^2)小于等于1/4
(1)
令a=b=x/2
f(x)=f(x/2)*f(x/2)=[f(x/2)]^2
非零函数f(x)
所以f(x)>0
(2)
令a=x1-x2 b=x2 且x10 f(x2)>0]
f(x1)/f(x2)>1
f(x1)>f(x2)
即得当x1f(x2)
所以f(x)为减函数
(3)
f(4)=f(2)*f(2) f(2)>0
所以f(2)=1/4
f(x-3)*f(5-x^2)
(1)f(-1+0)=f(-1)*f(0),f(-1)>1,f(0)=1
另x>0,f(0)=f(x+(-x))=f(x)*f(-x),f(x)=f(0)/f(-x),f(0)=1,f(-x)>1,
f(x)>0
(2)f(x-1)=f(x)*f(-1),f(x)>0,f(x-1)/f(x)=f(-1),f(-1)>1,所以f(x-1)>f(x),所以为减函数
(1)由题意得,当x<0时,f(x)>1,即f(x)>0;
当x=0时,取a=b=0,则f(0)=f(0)*f(0),又因为f(x)非零,则f(0)>0; 当x>0时,取a=b=x/2,则f(x)=f(x/2)*f(x/2)>0,故f(x)大于0;
(2)设b<0,则a+b
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(1)由题意得,当x<0时,f(x)>1,即f(x)>0;
当x=0时,取a=b=0,则f(0)=f(0)*f(0),又因为f(x)非零,则f(0)>0; 当x>0时,取a=b=x/2,则f(x)=f(x/2)*f(x/2)>0,故f(x)大于0;
(2)设b<0,则a+b1,所以f(a)/f(a+b)<1,即f(a)
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