What is the inverse of f(x)=e^{-(x^2)/2} ?

The inverse of f(x)=e^{-(x^2)/2} is 2^{1/2}(-ln(x))^{1/2},-2^{1/2}(-ln(x))^{1/2}

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inverse of f(x)=e^{-(x^2)/2}

inverse

f (x) = e^{- \frac{x ^{2}}{2}}

2^{\frac{1}{2}} (- ln (x))^{\frac{1}{2}}, - 2^{\frac{1}{2}} (- ln (x))^{\frac{1}{2}}

Solution steps

y = e^{- \frac{x ^{2}}{2}}

Replace

x

with

y

x = e^{- \frac{y ^{2}}{2}}

Solve for

y, x = e^{- \frac{y ^{2}}{2}}

2^{\frac{1}{2}} (- ln (x))^{\frac{1}{2}}, - 2^{\frac{1}{2}} (- ln (x))^{\frac{1}{2}}

f (x) = 9 x^{2} - 3

f (x) = e^{2 x} + 5

f (x) = - 7 cos (2 x), 0 \leq x \leq \frac{π}{2}

lo g_{\frac{5}{4}} (5 x - 4 x^{2})

f (x) = \frac{- 10 x + 1}{9 x + 6}

What is the inverse of f(x)=e^{-(x^2)/2} ?
The inverse of f(x)=e^{-(x^2)/2} is 2^{1/2}(-ln(x))^{1/2},-2^{1/2}(-ln(x))^{1/2}