SOLUTION: I could use some help with this problem please.Determine f^-1 for f(x)=∛(x+5. It's cubed if it is too small to see. Thank you

Algebra ->  Graphs -> SOLUTION: I could use some help with this problem please.Determine f^-1 for f(x)=∛(x+5. It's cubed if it is too small to see. Thank you      Log On


   

Question 529535: I could use some help with this problem please.Determine f^-1 for
f(x)=∛(x+5. It's cubed if it is too small to see. Thank you
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

f%5E%28-1%29%28x%29+=+root%283%2C+%28x%2B5%29%29+ you refer to the inverse of the function f(x).
Given y+=+root%283%2C+%28x%2B5%29%29

to find an inverse of f(x) you will need interchange the x and y:
x+=+root%283%2C+%28y%2B5%29%29

now solve for y:
To undo the cube root, you must cube both sides:
x+=+%28root%283%2C+%28y%2B5%29%29%29%5E3
x%5E3+=+y%2B5+
x%5E3+-+5+=+y
or
y=x%5E3+-+5+
This new y+ that you just solved for the the inverse function for f%28x%29; so, the inverse function for f%28x%29+=root%283%2C+%28y%2B5%29%29+ is f%5E%28-1%29+%28x%29+=+x%5E3+-+5+