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Functions, EXT1 F1 2010 HSC 3b*

Let  .  The diagram shows the graph  .
 

 Inverse Functions, EXT1 2010 HSC 3b

  1. The graph has two points of inflection.  

     

    Find the    coordinates of these points.   (3 marks)

  2. Explain why the domain of    must be restricted if    is to have an inverse function.    (1 mark)

  3. Find a formula for    if the domain of    is restricted to  .   (2 marks)

  4. State the domain of  .    (1 mark)

  5. Sketch the curve  .    (1 mark)

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  1.  
  5.  
  6. Inverse Functions, EXT1 2010 HSC 3b Answer
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i.   
 
 
   
   

 

 
   
 
   
COMMENT: It is also valid to show that is an even function and if a P.I. exists at , there must be another P.I. at .
 

 

 

ii.  
 
 
 

 

iii.  

 

 

 


 

♦ Parts (iv) and (v) were poorly answered with mean marks of 39% and 49% respectively.
iv.  

 

v. 

Inverse Functions, EXT1 2010 HSC 3b Answer

Functions, EXT1 F1 2007 HSC 6b

Consider the function  .

  1. Show that    is increasing for all values of .  (1 mark)

  2. Show that the inverse function is given by
     
     (3 marks)

  3. Hence, or otherwise, solve  . Give your answer correct to two decimal places.  (1 mark)

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i.   
 

 

 
 

 

 

ii. 

 

 

 

 

  

iii.