Inverting Functions

To find the inverse of a function  
\[f(x)\]

1. Replace  
\[f(x)\]
  by  
\[y\]
.
2. Make  
\[x\]
  the subject.
3. Swap  
\[x\]
  and  
\[y\]
  over.
4. Replace  
\[y\]
  by  
\[f^{-1}(x)\]

Example:  
\[f(x)=x^2-1\]

1.
\[y=x^2-1\]

2.
\[x=\sqrt{y+1}\]

3.
\[y=\sqrt{x+1}\]

4.
\[f^{-1}(x)= \sqrt{x+1}\]

To get the graph of  
\[f^{-1}(x)\]
  reflect the graph of  
\[f(x)\]
  in the line  
\[y=x\]