What is the inverse of f(x)=ln(4-sqrt(x^2-9)) ?

The inverse of f(x)=ln(4-sqrt(x^2-9)) is sqrt(-8e^x+e^{2x)+25},-sqrt(-8e^x+e^{2x)+25}

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inverse of f(x)=ln(4-sqrt(x^2-9))

inverse

f (x) = ln (4 - x^{2} - 9)

- 8 e^{x} + e^{2 x} + 25, - - 8 e^{x} + e^{2 x} + 25

Solution steps

y = ln (4 - x^{2} - 9)

Replace

x

with

y

x = ln (4 - y^{2} - 9)

Solve for

y, x = ln (4 - y^{2} - 9)

- 8 e^{x} + e^{2 x} + 25, - - 8 e^{x} + e^{2 x} + 25

x = - y^{3} - 2

lo g_{3} (- 2 x - 2) + 1

z \frac{1}{1 - z ^{- 1}}

f (x) = 11 - \frac{x}{4} h (x) = - 4 (x - 11)

f (x) = 59 ln (x)

What is the inverse of f(x)=ln(4-sqrt(x^2-9)) ?
The inverse of f(x)=ln(4-sqrt(x^2-9)) is sqrt(-8e^x+e^{2x)+25},-sqrt(-8e^x+e^{2x)+25}