inverse function

Question

Find the inverse function of f(x) =        3
                                                    ---------

                                                       x − 1
f −1(x) = _________

 

Use a graphing utility to find the domain and range of f −1(x).
Write the domain and range in interval notation

 

domain_______

range ________
     

Answer 1

Hi Jill,

 

I use 4 steps to find inverse functions.

 

1) Change f(x) to y

y = 3/(x-1)

 

2) changes x's to y's and y's to x's

x = 3/(y-1)

 

3) solve for y

x(y-1) = 3

y-1 = 3/x

y = (3/x) +1

 

4) change y to f^-1(x)

f^-1(x) = (3/x) + 1

 

The domain of f^-1(x) is all reals such that x≠0

If x=0 the function is undefined.

 

The range of f^-1(x) is all reals such that f^-1(x) ≠ -1 

Graph the function to see this.