SOLUTION: Find the inverse of f(x)=3x-5/2

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Question 1153262: Find the inverse of f(x)=3x-5/2
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the inverse of f%28x%29=3x-5%2F2
f%28x%29=y
y=3x-5%2F2.......swap variables
x=3y-5%2F2.........solve for y
x%2B5%2F2=3y
y=x%2F3%2B%285%2F2%29%2F3
y=x%2F3%2B5%2F6
inverse: f%5E-1%28x%29=x%2F3%2B5%2F6

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


Tutor @MathLover1 has shown finding the inverse by the traditional formal algebraic method -- switching the x and y and solving for the new y.

For many relatively simple functions, it is far easier to find the inverse using the idea that an inverse "gets you back where you started from".

To "get you back where you started from", an inverse function has to perform the opposite operations in the opposite order, compared to the original function.

In this example, the function does the following operations on the input:
(1) multiply by 3
(2) subtract 5/2

So the inverse function has to
(1) add 5/2
(2) divide by 3

So the inverse function is %28x%2B5%2F2%29%2F3+=+%281%2F3%29x+%2B+5%2F6

Much less work than the formal algebraic method....