SOLUTION: Find the inverse of the one-to-one function.
f(x)=3x+1/4
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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) (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) (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
Change the format if desired or required....
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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
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