Найти функцию, обратную данной

[latex]f(y)=1-e^{\frac{y^2}{2\sigma^2}}\\\\e^{\frac{y^2}{2\sigma ^2}}=1-f(y)\\\\\frac{y^2}{2\sigma ^2}=ln(1-f(y))\\\\y^2=2\sigma ^2\cdot ln(1-f(y))\\\\y^2=\sigma ^2\cdot ln(1-f(y))^2\; ,\; \; oboznachim\; \; z=f(y)\\\\y^2=\sigma ^2\cdot ln(1-z)^2\\\\Obratnaya\; fynkciya:\; \; z^2=\sigma ^2\cdot ln(1-y)^2[/latex]