SOLUTION: Find the inverse of f(x)=x^3+1 Please explain line by line step by step explanation. Thank you.

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Question 1140512: Find the inverse of f(x)=x^3+1
Please explain line by line step by step explanation. Thank you.
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3%2B1
y+=+x%5E3+%2B+1
to find the inverse, swap x and y
x+=+y%5E3+%2B+1
solve for y
y^3 = x - 1
Find the cube root of both sides
y = 3sqrt%28x-1%29
f%28x%5E-1%29+=+3sqrt%28x-1%29

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


The other tutor showed you the standard method for finding the inverse of a function: switch x and y and solve for the new y.

For many relatively simple functions, you can find the inverse easily using the fact that an inverse function "gets you back where you started".

For an inverse function to get you back where you started, it has to perform the opposite operations and in the opposite order, compared to the given function.

In this example, the operations performed by the given function are
(1) cube the input; and
(2) add 1

The inverse function then has to
(1) subtract 1; and
(2) take the cube root

So the inverse function for this example is

y+=+root%283%2Cx-1%29