设函数f(x)= a*2^x-1/2^x+1满足f - 知识问答

设函数f(x)= a*2^x-1/2^x+1满足f(-x)=-f(x) 求实数a的值求f(x)的反函数f-1(x)

1个回答

f(x)=(a*2^x-1)/(2^x+1)满足f(-x)=-f(x) ;f(0)=(a-1)/2=0
a=1
f(x)=(2^x-1)/(2^x+1);x∈R
f-1(x)=log2 (1+x)/(1-x);x∈(-1,1)
f-1(x)>log2(1+x) ;log2 (1+x)/(1-x)>log2(1+x)
log2(1-x)

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