SOLUTION: How do i find the inverse of f(x) = 1/2 (x-2)³ +3

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Question 1022638: How do i find the inverse of f(x) = 1/2 (x-2)³ +3

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will assume the function is +f%28x%29+=+%281%2F2%29%28x-2%29%5E3+%2B3+
This function is one-to-one in its domain, hence its inverse function will exist.
Now let +y+=+%281%2F2%29%28x-2%29%5E3+%2B3+
==> +y-3=+%281%2F2%29%28x-2%29%5E3+
==> 2y-6+=+%28x-2%29%5E3+
==> root%283%2C+2y-6%29+=+x-2 after taking cube roots of both sides.
==> root%283%2C+2y-6%29+%2B+2+=+x
Now interchange the positions of x and y:
root%283%2C+2x-6%29+%2B+2+=+y
This is the inverse function of +f%28x%29+=+%281%2F2%29%28x-2%29%5E3+%2B3+