若x=0,則f(x)=2^x-1/2^x 1由f(x)=2知,x>=0,令n=2^x,則n>=1 f(x)=n-1/n=2,得n^2-2n-1=0,則2^x=n=(2+2根號(hào)2)/2=1+根號(hào)2 則x=log2(1+根號(hào)2) 2令F(t)=2^tf(2t)+mf(t)=2^t(2^(2t)-1/2^(2t))+m(2^t-1/2^t) 令a=2^t,則當(dāng)tE[1,2]時(shí),aE[1,4] 則F(t)=m(a-1/a)+a^3-1/a>=0 且a>=1,則a-1/a>=0 則m>=(1/a-a^3)/(a-1/a),分子是a的減函數(shù),分母是a的增函數(shù) 則只要m>=(1/4-4^3)/(4-1/4)即可 即m>=-17