f ( x ) = x \cdot e ^ { - 1,5 x ^ { 2 } }
Solve for f
\left\{\begin{matrix}\\f=e^{-\frac{3x^{2}}{2}}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{-6\ln(f)}}{3}\text{; }x=-\frac{\sqrt{-6\ln(f)}}{3}\text{, }&f>0\text{ and }f\leq 1\end{matrix}\right.
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xf=xe^{-\frac{3x^{2}}{2}}
The equation is in standard form.
\frac{xf}{x}=\frac{xe^{-\frac{3x^{2}}{2}}}{x}
Divide both sides by x.
f=\frac{xe^{-\frac{3x^{2}}{2}}}{x}
Dividing by x undoes the multiplication by x.
f=e^{-\frac{3x^{2}}{2}}
Divide xe^{-\frac{3x^{2}}{2}} by x.
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