Funkcja odwrotna

[yolo123]

Jak wyznaczyć funkcję odwrotną do danej\(\displaystyle{ f(x)= \frac{e^x-e^{-x}}{e^x+e^{-x}}}\)?

[Benny01]

\(\displaystyle{ y=\frac{e^{2x}-1}{e^{2x}+1}}\)

\(\displaystyle{ y+ye^{2x}=e^{2x}-1}\)

\(\displaystyle{ y+1=e^{2x}(1-y)}\)
\(\displaystyle{ \frac{1+y}{1-y}=e^{2x}}\)
\(\displaystyle{ x=\frac{1}{2} \cdot \ln \frac{1+y}{1-y}}\)

[Richard del Ferro]

\(\displaystyle{ f(x)=\tg(x) \cdot i}\)

\(\displaystyle{ \frac{y}{i} =\tg(x)}\)

\(\displaystyle{ x=\arctg \frac{y}{i}}\)

[a4karo]

\(\displaystyle{ f(x)=\tg(x) \cdot i}\)

Coś Ci tu nie wyszło....

[PoweredDragon]

\(\displaystyle{ y = \tanh x}\)
\(\displaystyle{ x = \ar \tgh y = \frac{1}{2} \ln \frac{1+y}{1-y}}\)