Question

已知f(x)=2^x,g(x)=4^x,求满足g[g(x)]＞f[f(x)]的x范围

Answer 1

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

g(x)=4^x=2^2x,g(g(x))=2^(2*2^2x)=2^(2^(2x+1))

g(g(x))>f(f(x))

则2^(2^(2x+1))>2^(2^x)

由指数函数的单调性

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

则2x+1>x

故x