Inverse Functions Wrap Up Wrap Up:

Notation for Inverse of 𝑓(𝑥):____________ Inverses switch the _____________ and the _______________. Graphs of inverses are reflected over the line ______________.

You can test to see if a function is actually the inverse of another function by…

Find the inverse of the relation or function given 1) 𝑓 𝑥 = 1,3 , 1,−1 , 1,−3 , (1,1) Is 𝑓(𝑥) a function? ________

𝑓!! 𝑥 = Is 𝑓!!(𝑥) a function? _______ 2) ℎ 𝑥 = !

!𝑥 + 2 3) 𝑦 = 2𝑥! + 3

Inverse Stations

Station  1  Find  Inverse:  

     Domain  𝑓(𝑥):      

Domain  𝑓!!(𝑥):    

Range  𝑓(𝑥):   Range  𝑓!!(𝑥):      

Is  the  Inverse  a  function?  

 

Station  2  Find  Inverse:  

     Domain  𝑓(𝑥):      

Domain  𝑓!!(𝑥):    

Range  𝑓(𝑥):   Range  𝑓!!(𝑥):      

Is  the  Inverse  a  function?    

Station  3  a.    Find  an  equation  for  the  inverse  of  the  function.        

 b.    Find   𝑓 ∘ 𝑓!! (3)  

   c.    Find   𝑓 ∘ 𝑓!! (𝑥)  

   d.    Find   𝑓!! ∘ 𝑓 (𝑥)    

 e.    Graph  the  inverse  of  the  following  function:    

 

 

Station  4  Find  Inverse:  

     Domain  𝑓(𝑥):      

Domain  𝑓!!(𝑥):    

Range  𝑓(𝑥):   Range  𝑓!!(𝑥):      

Is  the  Inverse  a  function?    

Station  5  Find  Inverse:  

     Domain  𝑓(𝑥):      

Domain  𝑓!!(𝑥):    

Range  𝑓(𝑥):   Range  𝑓!!(𝑥):      

Is  the  Inverse  a  function?                          

Station  6  Use  the  graph  to  determine  the  following:                          f.    Graph  the  inverse  of  the  following  function: