SOLUTION: Find the inverse of the one-to-one function. f(x) = 2x-1 _____ 7

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Question 1135783: Find the inverse of the one-to-one function.
f(x) = 2x-1
_____
7
Found 3 solutions by jim_thompson5910, greenestamps, MathTherapy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%282x-1%29%2F7 Original function

y+=+%282x-1%29%2F7 Replace f(x) with y

x+=+%282y-1%29%2F7 Swap x and y; from here we solve for y

7x+=+2y-1 Multiply both sides by 7

7x%2B1+=+2y Add 1 to both sides

2y+=+7x%2B1 Swap both sides

y+=+%287x%2B1%29%2F2 Divide both sides by 2

Replace y with inverse function notation

--------------------------------------

The inverse is

Side note: This is the same as writing

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(Revised response -- I didn't recognize that the
   -----

   7

was part of the function.)

The method commonly taught (and commonly used) for finding the inverse of a function is as shown by the other tutor: switch the x and y and solve for the new y.

Here is an alternative to that method which is much faster and easier and works for many relatively simple functions.

The inverse of a function "gets you back where you started". To do that, the inverse must perform the opposite operations in the opposite order.

The given function performs the following operations on the input:
(1) multiply by 2;
(2) subtract 1;
(3) divide by 7

So the inverse function needs to
(1 multiply by 7;
(2) add 1;
(3) divide by 2

The inverse function is f^-1(x) = (7x+1)/2, or (7/2)x+1/2.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the inverse of the one-to-one function.
f(x) = 2x-1
_____
7


Correct answer: 

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