Expert: Paul Klarreich - 10/18/2008

Question
Given  f (x) = (2x + 1) / 3   find f -1(x).

Answer
Questioner:   Sharon
Category:  Calculus
Private:  No
 
Subject:  Calculus 1
Question:  Given  f (x) = (2x + 1) / 3   find f -1(x).
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Hi, Sharon,

I assume you want the inverse function.  You didn't tell me what you were studying, so I have to guess.

To find the inverse:

1. Write y = ... instead of f(x) =....

2. Exchange the variables x and y.

3. Solve the new equation for  y.

4. Write  f-inv(x) = ... instead of  y = ...


f(x) = (2x + 1)/3

y = (2x + 1)/3

x = (2y + 1)/3

2y + 1 = 3x

2y = 3x - 1

    3x - 1
y =  ------
       2
           3x - 1
f-inv(x) =  ------
              2