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

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

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

inverse

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

ln (4 x^{2} - 4)

Solution steps

y = \frac{e ^{x} + 4}{2}

Replace

x

with

y

x = \frac{e ^{y} + 4}{2}

Solve for

y, x = \frac{e ^{y} + 4}{2}

ln (4 x^{2} - 4)

\frac{1 + 7 x}{7 - 5 x}

x^{2} = 2 y

\frac{( 2 x + 3 )}{( 7 x - 8 )}

g (x) = \frac{4}{x - 2} + 3

f (x) = (x + 8)^{2} - 3

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