SOLUTION: I have this question, but I'm not sure how to solve it because it is cubed, I'm pretty sure its squared but I still dont know how to solve it. Someone please help me, thank you!!

Algebra ->  Functions -> SOLUTION: I have this question, but I'm not sure how to solve it because it is cubed, I'm pretty sure its squared but I still dont know how to solve it. Someone please help me, thank you!!       Log On


   

Question 106807: I have this question, but I'm not sure how to solve it because it is cubed, I'm pretty sure its squared but I still dont know how to solve it. Someone please help me, thank you!!
Find the inverse for +f%28x%29+=+x%5E3%2B1+ , and verify that the functions are inverses of each other.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the inverse and verify:
f%28x%29+=+x%5E3%2B1 Change the f(x) to y, then interchange the x and y.
y+=+x%5E3%2B1
x+=+y%5E3%2B1 Now solve this for y.
y%5E3+=+x-1 Take the cube root of both sides.
y+=+%28x-1%29%5E%281%2F3%29 Now change the y to f%5E%28-1%29%28x%29.
f%5E%28-1%29%28x%29+=+%28x-1%29%5E%281%2F3%29
Check:
Show 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%281%2F3%29%29 = %28%28x-1%29%5E%281%2F3%29%29%5E3%2B1+=+%28x-1%29%2B1 = x