What is the inverse of f(x)=3ln(sqrt(5x-2)+6) ?

The inverse of f(x)=3ln(sqrt(5x-2)+6) is (e^{(2x)/3}-12e^{x/3}+38)/(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse of f(x)=3ln(sqrt(5x-2)+6)

inverse

f (x) = 3 ln (5 x - 2 + 6)

\frac{e ^{\frac{2 x}{3}} - 12 e ^{\frac{x}{3}} + 38}{5}

Solution steps

y = 3 ln (5 x - 2 + 6)

Replace

x

with

y

x = 3 ln (5 y - 2 + 6)

Solve for

y, x = 3 ln (5 y - 2 + 6)

\frac{e ^{\frac{2 x}{3}} - 12 e ^{\frac{x}{3}} + 38}{5}

y = - 4 - 2 x + 1 - 2

g (x) = \frac{x}{5} + 2

f (x) = - 0.1 x^{2} + 90

f (x) = - \frac{1}{2} (\frac{1}{2})^{x} + 7

f (x) = arccos (e) (e^{3 x})

What is the inverse of f(x)=3ln(sqrt(5x-2)+6) ?
The inverse of f(x)=3ln(sqrt(5x-2)+6) is (e^{(2x)/3}-12e^{x/3}+38)/(5)