Homework Help

Question

Find the inverse of each function:

f(x)=3^x+2

g(x)=log _7X-2

 

Solve Each equation:

log(3x-2)=2

e^x+2=8

 

Answer 1

The inverse the function:
f(x)=3^x+2

Step 1: Replace the function notation with y. y=3^x+2

Step 2: Switch x and y.       x = 3^y+2

Step 3: Solve for y.             x -2 = 3^y

                                         log₃(x - 2)= y

The inverse function is: f^-1(x) = log₃(x-2) 

 

g(x)=log _7X-2  (Not clear what the dash _ is for??)


log(3x-2)=2

Rewrite in exponential form: 10²= 3x -2

SOLVE:   100= 3x - 2

                                              102=3x

34=x

e^x+2=8

Isolate the variable term: e^x = 6

Rewrite as natural log:   ln(6) = x

Evaluate:                        x ≅ 1.792