Find the inverse of each of the following functions fx ln3x

Find the inverse of each of the following functions: f(x) = ln(3x - 2) + 1 g(x) = 2Squareroote^x - 5

Solution

2)

a) let f(x)=y => x =f^-1(y)

ln(3x -2) +1=y

ln(3x -2)=y -1

3x-2=e^y-1

3x=2+e^y-1

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

f^-1(y)=(1/3)[2+e^y-1]

f^-1(x)=(1/3)[2+e^x-1]

b)let f(x)=y => x =f^-1(y)

2(e^x-5)=y

(e^x-5)=y/2

(e^x-5)=(y/2)²

e^x=5+(y/2)²

x=ln(5+(y/2)²)

f^-1(y)=ln(5+(y/2)²)

f^-1(x)=ln(5+(x/2)²)