SOLUTION: Find the inverse of the function f(x) = x1/3 + 2. a. (x - 2)3 b. x1/3 + 2 c. (y - 2)3 d. Doesn’t exist this should be easy but I'm struggling with it.

Algebra ->  Rational-functions -> SOLUTION: Find the inverse of the function f(x) = x1/3 + 2. a. (x - 2)3 b. x1/3 + 2 c. (y - 2)3 d. Doesn’t exist this should be easy but I'm struggling with it.       Log On


   

Question 83096This question is from textbook
: Find the inverse of the function f(x) = x1/3 + 2.
a. (x - 2)3
b. x1/3 + 2
c. (y - 2)3
d. Doesn’t exist
this should be easy but I'm struggling with it.
 This question is from textbook

Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
This is a very problem and the solution for this goes this way:

To find the inverse of the given function.

f(x) = %28x%5E%281%2F3%29%29+%2B+2

Let y = f(x) = %28x%5E%281%2F3%29%29+%2B+2


y = %28x%5E%281%2F3%29%29+%2B+2

Replacing x and y we get:

x = %28y%5E%281%2F3%29%29+%2B+2

Solving for y, further we get:

x - 2 = %28y%5E%281%2F3%29%29

Taking the cube root on both sides, we get:

y = %28x+-+2%29%5E3

Thus, the inverse value is:

%28f%5E-1+%28x%29%29 = %28x+-+2%29%5E3


Hence, the solution..


Happy Calculating!!

Hence, the exact answer for the given problem among the given choices is (a)