text: # Precalculus, Enhanced WebAssign Edition (6th Edition) View more editions Solutions for Chapter 4.FOM
  
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  • Step 1 of 19
  
  Consider
  
  • Step 2 of 19
  
  (a)
  
  To find the domain of determine the values that would make the function undefined.
  
  Because there are no values that make the function undefined, conclude that the domain of the function is.
  
  • Step 3 of 19
  
  (b)
  
  To find the domain of we can determine the values that would make the function undefined.
  
  Given function is a function with square root. The value under the radical is always positive.
  
  Therefore, conclude that cannot less than -4. Because of this fact, conclude that the domain of the function is
  
  • Step 4 of 19
  
  (c)
  
  To determine, simply plug -2 into as shown below:
  
  • Step 5 of 19
  
  To determine, simply plug 0 into as shown below:
  
  • Step 6 of 19
  
  To determine, simply plug 4 into as shown below:
  
  • Step 7 of 19
  
  To determine, simply plug 4 into as shown below:
  
  • Step 8 of 19
  
  To determine, simply plug 4 into as shown below:
  
  • Step 9 of 19
  
  To determine, we can simply plug 4 into as shown below:
  
  Because the value under the radical is negative, the value of the function is undefined.
  
  • Step 10 of 19
  
  (d)
  
  To determine, simply plug into as shown below:
  
  To determine, simply plug into as shown below:
  
  • Step 11 of 19
  
  To determine, simply plug into as shown below:
  
  • Step 12 of 19
  
  (e)
  
  The formula for the average rate of change is given below:
  
  Average rate of change =
  
  • Step 13 of 19
  
  Using the equation above, we can solve for the rate of change as shown below:
  
  • Step 14 of 19
  
  First solve for and.
  
  • Step 15 of 19
  
  Using these values we can now solve for the average rate of change as shown below:
  
  • Step 16 of 19
  
  (f)
  
  Find the composition of with. The value is as follows.
  
  • Step 17 of 19
  
  Similarly the composition ofwith is as follows.
  
  • Step 18 of 19
  
  Now find the values of
  
  And
  
  • Step 19 of 19
  
  (g)
  
  Consider
  
  Let us assume that
  
  The value under the radical is always positive. So,
  
  Calculate the inverse as follows.
  
  Squaring on both sides
  
  Subtract 4 on both sides
  
  It is noted that
  
  Now interchange.
  
  Therefore, the inverse of the function,
  
  Corresponding Textbook
  
  Precalculus, Enhanced WebAssign Edition | 6th Edition
  9781133594765ISBN-13: 113359476XISBN: Authors:
  Alternate ISBN: 9781133954750, 9781285499949