What is the inverse of f(x)=(4ln(x^2))/(e^2) ?

The inverse of f(x)=(4ln(x^2))/(e^2) is sqrt(e^{(xe^2)/4)},-sqrt(e^{(xe^2)/4)}

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inverse of f(x)=(4ln(x^2))/(e^2)

inverse

f (x) = \frac{4 ln ( x ^{2} )}{e ^{2}}

e^{\frac{x e ^{2}}{4}}, - e^{\frac{x e ^{2}}{4}}

Solution steps

y = \frac{4 ln ( x ^{2} )}{e ^{2}}

Replace

x

with

y

x = \frac{4 ln ( y ^{2} )}{e ^{2}}

Solve for

y, x = \frac{4 ln ( y ^{2} )}{e ^{2}}

e^{\frac{x e ^{2}}{4}}, - e^{\frac{x e ^{2}}{4}}

What is the inverse of f(x)=(4ln(x^2))/(e^2) ?
The inverse of f(x)=(4ln(x^2))/(e^2) is sqrt(e^{(xe^2)/4)},-sqrt(e^{(xe^2)/4)}