f(x)=3tan2x和f(x)=e^x/e^x+1的反函数怎么求?

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f(x)=3tan2x和f(x)=e^x/e^x+1的反函数怎么求?
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f(x)=3tan2x和f(x)=e^x/e^x+1的反函数怎么求?
f(x)=3tan2x和f(x)=e^x/e^x+1的反函数怎么求?

f(x)=3tan2x和f(x)=e^x/e^x+1的反函数怎么求?

y=3tan2x
tan2x=y/3
2x=arctany/3
x=1/2arctany/3
反函数:y=1/2arctanx/3 定义域R
y=e^x/(e^x+1)
e^x=y*e^x+y
e^x(1-y)=y
e^x=y/(1-y)
x=ln(y/(1-y))
反函数 y=ln(x/(1-x)) 定义域 (0,1)