SOLUTION: Find the inverse of the function f(x)= x ^1/3 + 2. I am so confused!! Can someone please help me????? FR a)(x-2) ^ 3 b)x ^1/3 + 2 c)(y-2) ^ 3 d)Doesn't exist

You not only need to learn how to get the inverse,
but mainly you need to learn just what you have when
you get the inverse function. 

Let's draw the graph of y = f(x) first so we'll be
able to see just what the inverse function is, not
just how to get it.



Rules for finding the inverse of a function:

1. Substitute y for f(x)
2. Interchange x and y
3. Solve for y.
4. Replace y by f-1(x)

f(x) = 

Following the four rules above:

1. y = 

2. x = 

3.   = x

         = x - 2

     Raise both sides to the 3rd power:

     = (x - 2)³

    y = (x - 2)³   

4.    f-1(x) = (x - 2)³ 

That's the answer, choice (a) But don't stop 
there, for you MUST understand what inverse
means.

So, let's draw the graph
of y = f-1(x) on the same set of
axes.  I'll draw it in green:



Notice that the green inverse curve is shaped just like 
the original red curve.  The graph of the inverse of a 
function is the reflection of the graph of the original 
function reflected into the identity line, whose equation
is y = x (setting the two letters y and x identically equal).

Here is the graph of the identity line y = x.



Putting it on the same set of axes with the function
and its inverse, we can see thet the green inverse curve 
is a reflection of the original function's red curve in the
blue identity line.


 
Edwin