What is the inverse of f(x)=ln(x^2-4)+pi,x<-2 ?

The inverse of f(x)=ln(x^2-4)+pi,x<-2 is sqrt(e^{x-pi)+4},-sqrt(e^{x-pi)+4}

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inverse of f(x)=ln(x^2-4)+pi,x<-2

inverse

f (x) = ln (x^{2} - 4) + π, x < - 2

e^{x - π} + 4, - e^{x - π} + 4

Solution steps

y = ln (x^{2} - 4) + π

Replace

x

with

y

x = ln (y^{2} - 4) + π

Solve for

y, x = ln (y^{2} - 4) + π

e^{x - π} + 4, - e^{x - π} + 4

f (x) = \frac{2 x}{5} + \frac{3}{2}

5 (x - 2)

\frac{x + 5}{x + 4}

f (x) = 15 - 6 x^{3}

f (x) = - 5 - x

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