Please help me find the inverse of the function.


The graph of the inverse of a function is the reflection
of the graph across the line whose equation is y = x which
is called the "identity line", because y and x are 
identically equal on that line.

So we'll be able to check that when we finish, we first
graph the equation by getting points, plotting them and
drawing a smooth curve through them. 





Now we follow the rules for finding the inverse:

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

1. Replace f(x) by y




2. Interchange x and y



3. Solve for y

 

Multiply both sides by 





Get all terms in y on the right and
all others on left:



Factor out y on the right



Divide both sides by 



Swap sides for convenience 



4. Replace y by f-1(x)

f-1(x) = 

Now let's graph this on the same set of
axes in green:



Now we'll draw in the identity line whose equation is y = x. 
We'll draw it dotted just to see if the green graph is the 
reflection of the dark red one in that dotted identity line:



Yes it is, so f-1(x) =  must be right. 

Edwin