已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1.令f(x)=g(x+已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1。令f(x)=g(x+1/2)+mlnx+9/8(m为R x大于0)求g(x)表达式2.若存在X大
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![已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1.令f(x)=g(x+已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1。令f(x)=g(x+1/2)+mlnx+9/8(m为R x大于0)求g(x)表达式2.若存在X大](/uploads/image/z/5304663-63-3.jpg?t=%E5%B7%B2%E7%9F%A5%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0g%28x%29%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%E9%83%BD%E6%BB%A1%E8%B6%B3g%28x-1%29%2Bg%281-x%29%3Dx2-2x-1%2C%E4%B8%94g%281%29%3D-1.%E4%BB%A4f%28x%29%3Dg%28x%2B%E5%B7%B2%E7%9F%A5%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0g%28x%29%E5%AF%B9%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0x%E9%83%BD%E6%BB%A1%E8%B6%B3g%28x-1%29%2Bg%281-x%29%3Dx2-2x-1%2C%E4%B8%94g%281%29%3D-1%E3%80%82%E4%BB%A4f%28x%29%3Dg%28x%2B1%2F2%29%2Bmlnx%2B9%2F8%28m%E4%B8%BAR+x%E5%A4%A7%E4%BA%8E0%EF%BC%89%E6%B1%82g%28x%29%E8%A1%A8%E8%BE%BE%E5%BC%8F2.%E8%8B%A5%E5%AD%98%E5%9C%A8X%E5%A4%A7)
已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1.令f(x)=g(x+已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1。令f(x)=g(x+1/2)+mlnx+9/8(m为R x大于0)求g(x)表达式2.若存在X大
已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1.令f(x)=g(x+
已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1。令f(x)=g(x+1/2)+mlnx+9/8(m为R x大于0)
求g(x)表达式
2.若存在X大于0使f(x)小于等于0成立,求m取值。
3.设1小于X大于或等于m,H(x)=f(x)-(m-1)x,证明:对任意x1,x2属于〔m,1〕恒有[H(x1)-H(x2)]绝对值小于1
已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1.令f(x)=g(x+已知二次函数g(x)对任意实数x都满足g(x-1)+g(1-x)=x2-2x-1,且g(1)=-1。令f(x)=g(x+1/2)+mlnx+9/8(m为R x大于0)求g(x)表达式2.若存在X大
1.设g(x)=ax^+bx+c,
g(1)=a+b+c=-1,①
g(x-1)+g(1-x)
=a(x-1)^+b(x-1)+c
+a(1-x)^+b(1-x)+c
=2ax^-4ax+2a+2c
=x^-2x-1,
比较系数得2a=1,2a+2c=-1,
解得a=1/2,c=-1,
代入①,b=-1/2.
∴g(x)=(1/2)x^-(1/2)x-1.
2.存在x>0,使得f(x)=g(x+1/2)+mlnx+9/8=(1/2)x^+mlnx>=0,
x=1时上述不等式恒成立,
∴m的取值范围是R.
3.H(x)=f(x)-(m-1)x=(1/2)x^-(m-1)x+mlnx,x∈[m,1],m>0,
H'(x)=x-(m-1)+m/x
=[x^-(m-1)x+m]/x
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