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

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

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

inverse

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

e^{x} + 2, - e^{x} + 2

Solution steps

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

Replace

x

with

y

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

Solve for

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

e^{x} + 2, - e^{x} + 2

\frac{3}{2} x^{2} + \frac{9}{2} x

f (y) = 3 x^{2} + x

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

f (x) = ln (x + 1) - 4

f (x) = \frac{5 x - 11}{10}

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