Find the inverse

Question

find the inverse, f^-1(x). For the equation f(x)=2e^3x+1

Answer 1

f(x) = 2e^3x+1

 

y = 2e^3x+1

 

To find the inverse function, f^-1(x), swap the x's and y's and solve for y:

 

x = 2e^3y+1

 

x-1 = 2e^3y

 

(1/2)(x-1) = e^3y

 

ln[(1/2)(x-1)] = 3y              [take the ln of both sides]

 

(1/3)(-ln(2)+ln(x-1)) = y      [ln(1/2) = ln(2^-1) = -ln(2), ln(ab) = ln(a) + ln(b)]

 

y = f^-1(x) = (1/3)ln(x-1) - (1/3)ln(2)