What is the inverse of f(x)=sqrt(4-e^{2x)} ?

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

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inverse of f(x)=sqrt(4-e^{2x)}

inverse

f (x) = 4 - e^{2 x}

\frac{ln ( 4 - x ^{2} )}{2}

Solution steps

y = 4 - e^{2 x}

Replace

x

with

y

x = 4 - e^{2 y}

Solve for

y, x = 4 - e^{2 y}

\frac{ln ( 4 - x ^{2} )}{2}

f (x) = x + 3 + 4

f (x) = x + 3 + 2

f (x) = \frac{( x + 6 )}{( x + 16 )}

f (x) = - x + 9

- \frac{1}{2} \cdot ln (1 - 2 y)

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