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Functions, EXT1 F1 EQ-Bank 4

Let    for  .

  1. State the domain of  .  (1 mark)

  2. What is the equation of  ?  (3 marks)

  3. For the restricted domain, sketch the function and the inverse function on the same number plane below.
  4. Clearly identify all axis intercepts.  (2 marks)

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a.   


 

b.   

c.   

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a.   


 

b.   

 
 
 
 
 
 

 
c.   

Functions, EXT1 F1 2023 MET1 7

Consider . Part of the graph of    is shown below.
 

  1. State the range of .   (1 mark)
  2. Sketch the graph of the inverse function  on the axes above. Label any endpoints and axial intercepts with their coordinates.   (2 marks)
  3. Determine the equation of the domain for the inverse function  .   (2 marks)
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a.   

b.   

c.   

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a.   

b.   

c.   


 

 


♦ Mean mark (c) 48%.
MARKER’S COMMENT: Common error → writing the function as .

Functions, EXT1 F1 2021 HSC 12d

A function is defined by    for    in the domain  .

  1. Sketch the graph of    showing the  -  and  -intercepts.  (2 marks)

  2. Find the equation of the inverse function,  ,  and state its domain.  (3 marks)

  3. Sketch the graph of   .   (1 mark)

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  4.  
     
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i.   


 

 

ii.   

 

 

 

iii.

Functions, EXT1 F1 2004 HSC 5b*

The diagram below shows a sketch of the graph of  , where    for  .
 

Inverse Functions, EXT1 2004 HSC 5b

  1. On the same set of axes, sketch the graph of the inverse function,  .  (1 mark)
  2. State the domain of  .  (1 mark)

  3. Find an expression for    in terms of  .  (2 marks)

  4. The graphs of    and    meet at exactly one point  .

     

    Let  α  be the -coordinate of  . Explain why  α  is a root of the equation  .  (1 mark)

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i.  

Inverse Functions, EXT1 2004 HSC 5b Answer

ii.   


 

iii. 

 

 

 

iv.   

 

α

 

Functions, EXT1 F1 2018 HSC 13b

The diagram shows the graph  , for all real .
 


 

Consider the function  , for

The function    has an inverse. (Do NOT prove this.)

  1.  State the domain and range of    (2 marks)

  2.  Sketch the graph    (1 mark)

  3.  Find an expression for    (3 marks)

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i.   

♦♦ Mean mark part (i) 31%.


 

 

♦ Mean mark part (ii) 43%.

ii.  

 

iii. 

♦ Mean mark part (iii) 45%.

 

 

Functions, EXT1 F1 2008 HSC 5a

Let    for  .  This function has an inverse,  . 

  1.  Sketch the graphs of    and    on the same set of axes. (Use the same scale on both axes.)  (2 marks)

  2.  Find an expression for  .   (3 marks)

  3.  Evaluate  .   (1 mark)

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  1.  
    Inverse Functions, EXT1 2008 HSC 5a Answer

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i. 

Inverse Functions, EXT1 2008 HSC 5a Answer
ii.   

 

 

 
 
 

 

 

iii.   
   
   
   
   

Functions, EXT1 F1 2012 HSC 12b

Let   

  1.  Find the domain of  .   (1 mark)

  2.  Find an expression for the inverse function  .    (2 marks)

  3.  Find the points where the graphs    and    intersect.   (1 mark)

  4.  On the same set of axes, sketch the graphs    and    showing the information found in part (iii).   (2 marks)

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  4.   
    1. Inverse Functions, EXT1 2012 HSC 12b Answer
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i. 

 

ii. 

 

 

iii. 

 

 

 

iv.

Inverse Functions, EXT1 2012 HSC 12b Answer