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

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

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inverse of f(x)=ln(x^2-4)

inverse

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

e^{x} + 4, - e^{x} + 4

Solution steps

y = ln (x^{2} - 4)

Replace

x

with

y

x = ln (y^{2} - 4)

Solve for

y, x = ln (y^{2} - 4)

e^{x} + 4, - e^{x} + 4

4 x - 2 - 1

f (x) = ln (1 - x)

f (x) = x (1 - x^{2})^{\frac{1}{2}}

f (x) = e^{x + x^{2}}

f (x) = x^{2} + 8 x + 4

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