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

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

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inverse of f(x)= 1/(2pi)e^{-(1x^2)/2}

inverse

f (x) = \frac{1}{2 π} e^{- \frac{1 x ^{2}}{2}}

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

Solution steps

y = \frac{1}{2 π} e^{- \frac{1 \cdot x ^{2}}{2}}

Replace

x

with

y

x = \frac{1}{2 π} e^{- \frac{1 \cdot y ^{2}}{2}}

Solve for

y, x = \frac{1}{2 π} e^{- \frac{1 y ^{2}}{2}}

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

f (x) = \frac{1 - 3 x}{x + 2}

f (x) = 9000 \cdot x

y = 49 - 4 x^{2}

y = 2 x - 3

f (x) = 9 x^{2} + 4

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