Question

社a属于R,f(x)为奇函数,f(2x)=4的x方加1分之a乘4的x方加a减2 (1)求f(x)的反函数f的负1次方(x

Answer 1

f(2x)=[a*2^(2x)+a-2]/[2^(2x)+1]

f(x)=(a*2^x+a-2)/(2^x+1)

f(x)为奇函数,f(0)=(2a-2)/2=0,得 a=1

f(x)=(2^x-1)/(2^x+1)=y

得2^x=(y+1)/(1-y)>0,所以-1