SOLUTION: Find the inverse of the one-to-one function. f(x)=3x+1/4

Algebra ->  Inverses -> SOLUTION: Find the inverse of the one-to-one function. f(x)=3x+1/4      Log On


   

Question 1179073: Find the inverse of the one-to-one function.
f(x)=3x+1/4
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
quick way
x=3y+1/4
3y=x-1/4
y=(x-1/4)/3
y=x/3-1/12

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


The method shown by the other tutor is fine: switch the x and y in the given function and solve for the new y. That method is often needed for complicated functions.

For relatively simple functions like this, there is a much easier way to find the inverse, using the idea that the inverse function "gets you back where you started" by "un-doing" what the function does.

What does the given function do to the input?
(1) multiply by 3; and
(2) add 1/4

The inverse function has to undo those operations, using the inverse operations in the opposite order.

Inverse function:
(1) subtract 1/4; and
(2) divide by 3

ANSWER: The inverse function is
f%28x%29=%28x-1%2F4%29%2F3

Change the format if desired or required....

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

The words of explanation make this look like a long process. But here is all that is really involved:

given function: multiply by 3; add 1/4
inverse function: subtract 1/4; divide by 3