Question

已知函数f(x)的图像过点(3,5),且与函数g(x)=2^(1/2x-1/2)-a的图像关于y=x对称.

Answer 1

f(x)为g(x)的反函数

即：由y=2^(1/2x-1/2)-a得：x=2log2(y+a)+1

即f(x)=2log2(x+a)+1

1)代入点（3,5）得：5=2log2(3+a)+1,得：a=1

故f(x)=2log2(x+1)+1,定义域为x>-1

2)由f(x-1)+f(y-2)=2+2log2[x(y-1)]>f(y)+1=2+2log2(y+1)

得：log2[x(y-1)/(y+1)]>0

x(y-1)/(y+1)>1

令x+y=z,则有：(z-y)(y-1)/(y+1)>1

z>(y+1)/(y-1)+y=1+2/(y-1)+y=2+2/(y-1)+(y-1)

利用a+b>=2√(ab)得：z>2+2√2,