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}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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}