Let f and g be two real functions such that g is the inverse of f is defined as
how do I solve this?
Your help is deeply appreciated.
Thank you.
, calculate and select the correct option:Baltuilhe wrote:Good afternoon!
[tex]y=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}[/tex]
[tex]y=\frac{e^{x}-\frac{1}{e^{x}}}{e^{x}+\frac{1}{e^{x}}}[/tex]
[tex]y=\frac{\frac{e^{2x}-1}{e^{x}}}{\frac{e^{2x}+1}{e^{x}}}[/tex]
[tex]y=\frac{e^{2x}-1}{e^{2x}+1}[/tex]
[tex]y\cdot\left(e^{2x}+1\right)=e^{2x}-1[/tex]
[tex]y\cdot e^{2x}-e^{2x}=-1-y[/tex]
[tex]e^{2x}\cdot\left(y-1\right)=-\left(1+y\right)[/tex]
[tex]e^{2x}=\frac{y+1}{y-1}[/tex]
[tex]2x=\ln\left(\frac{y+1}{y-1}\right)[/tex]
[tex]x=g(y)=\frac{1}{2}\cdot\ln\left(\frac{y+1}{y-1}\right)[/tex]
Try to reach the answer, now
Good luck
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