Question

已知f(x)=2的x次方,g(x)=4的x次方,求满足g[f(x)]＞f[g(x)]的x取值范围.

Answer 1

答：

f(x)=2^x,g(x)=4^x

g [f(x)]=4^[f(x)]=4^(2^x)=2^(2*2^x)=2^[2^(x+1)]

f [g(x)]=2^[g(x)]=2^(4^x)=2^[2^(2x)]

g [f(x)]>f [g(x)]即是：

2^[2^(x+1)]>2^[2^(2x)]

所以：

2^(x+1)>2^(2x)

所以：x+1>2x

解得：x