Find the inverse function if it exists

Question

Find the inverse function (if it exists) of

f(x)=ln(5-6x)

f^-1(x)=

Answer 1

f(x) = ln(5-6x)

 

y = ln(5-6x)

 

Switch the x's and y's:

 

x = ln(5-6y)

 

Solve for y:

 

e^x = 5 - 6y             [Raised both sides as exponents of e]

 

e^x - 5 = -6y

 

(5-e^x)/6 = f^-1(x)

 

Check:

 

(f(f^-1(x)) =  ln[5-6((5-e^x)/6)] = ln(5-5+e^x) = x   CHECK!