What is the inverse of f(x)=(e^x)/(5+e^2) ?

The inverse of f(x)=(e^x)/(5+e^2) is ln(x(5+e^2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of f(x)=(e^x)/(5+e^2)

inverse

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

ln (x (5 + e^{2}))

Solution steps

y = \frac{e ^{x}}{5 + e ^{2}}

Replace

x

with

y

x = \frac{e ^{y}}{5 + e ^{2}}

Solve for

y, x = \frac{e ^{y}}{5 + e ^{2}}

ln (x (5 + e^{2}))

y = 3 x^{2} + 2

2 + 3 - x

f (x) = \frac{1}{6 x ^{2}}

f (x) = 6 - \frac{4 x}{1 + 3 x}

f (x) = (x - 9)^{2} + 3

What is the inverse of f(x)=(e^x)/(5+e^2) ?
The inverse of f(x)=(e^x)/(5+e^2) is ln(x(5+e^2))