SOLUTION: Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f inverse and vice-ve

Algebra ->  Inverses -> SOLUTION: Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f inverse and vice-ve      Log On


   

Question 1125605: Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f inverse and vice-versa.
f(x)=6-5∛(x-8)
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x.

y = 6 - 5cbrt(x - 8)
y - 6 = 5cbrt(x - 8)
(y-6)^3 = 125(x - 8)
(y-6)^3/125 = x - 8

f^(-1)(x) = ((x-6)^3/125) + 8