SOLUTION: Inverse Functions: For y=x^3+1 a) Find f^-1 b) Verify your answer by showing their compositions

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Question 390149: Inverse Functions:
For y=x^3+1
a) Find f^-1
b) Verify your answer by showing their compositions
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
For:
y+=+x%5E3%2B1+ find f%5E%28-1%29%28x%29 Exchange the x and y.
x+=+y%5E3%2B1 Solve for y.
y%5E3+=+x-1 Take the cube root of both sides.
y+=+%28x-1%29%5E%281%2F3%29 Replace the y with f%5E%28-1%29%28x%29
f%5E%28-1%29%28x%29+=+%28x-1%29%5E%281%2F3%29
Check to see that:
f%28f%5E%28-1%29%28x%29%29+=+x
f%28f%5E%28-1%29%28x%29%29+=+f%28%28x-1%29%5E%28-1%2F3%29%29=%28%28x-1%29%5E%281%2F3%29%29%5E3%2B1+=+%28x-1%29%2B1=x