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

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

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

inverse

f (x) = a \cdot e^{x^{2}}

ln (\frac{x}{a}), - ln (\frac{x}{a})

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = a \cdot e^{y^{2}}

ln (\frac{x}{a}), - ln (\frac{x}{a})

x + 5 + 2

x = - y + 6

\frac{9}{\frac{9}{x}}

y = 3 lo g_{6} (x)

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