SOLUTION: find the inverse of f(x)=2x^3+1

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Question 1181200: find the inverse of f(x)=2x^3+1
Found 3 solutions by MathLover1, mccravyedwin, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

find+the+inverse+of+%7B%7B%7Bf%28x%29=2x%5E3%2B1
recall that f%28x%29=y
y=2x%5E3%2B1......swap variables
x=2y%5E3%2B1.........solve for y
x-1=2y%5E3
%28x-1%29%2F2=y%5E3
y=root%283%2C%28x-1%29%2F2%29
inverse is
f'%28x%29=root%283%2C%28x-1%29%2F2%29



Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!
The red graph is the graph of f(x) = 2x3+1
The dotted line is the identity line y=x 
The green graph is the inverse f-1(x) = root%283%2C%28x-1%29%2F2%29

Note that the inverse of a function is its reflection in or across the
identity line.




f%28x%29=2x%5E3%2B1
y=2x%5E3%2B1
x=2y%5E3%2B1
x-1=2y%5E3
%28x-1%29%2F2=y%5E3

root%283%2C%28x-1%29%2F2%29=y
f-1(x) = root%283%2C%28x-1%29%2F2%29

Edwin

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


You have received two responses from tutors so far that both use the same method for finding the inverse of a function: switch the x and y and solve for the new y.

That is a standard method which you should know and understand.

For many relatively simple functions like this one, the inverse can be found more easily, without algebra, using the notion that an inverse function "un-does" what the function does.

In this example, the operations performed on the input by the given function are
(1) raise it to the 3rd power;
(2) multiply by 2; and
(3) add 1

The inverse function must undo those operations by performing the opposite operations in the opposite order:
(1) subtract 1: x-1
(2) divide by 2: %28x-1%29%2F2
(3) take the cube root: root%283%2C%28x-1%29%2F2%29

If you compare that informal method for finding the inverse to the formal mathematical method shown by the other tutors, you will see that EXACTLY the same work is being done; however, the path to the solution is easier and faster without the need for the formal algebra.