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

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

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

inverse

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

- ln (x), - - ln (x)

Solution steps

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

Replace

x

with

y

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

Solve for

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

- ln (x), - - ln (x)

f (x) = 4 x - 12

f (x) = 2 x + 6

y = x - 6

(0, 0), (- 2, 3)

f (x) = \frac{4 + x ^{4}}{x ^{2} - x ^{4}}

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