SOLUTION: <pre>Help! PAGE 131 #19 Find and simplify the difference quotient: f(x + h) - f(x) ----------- -----, h does not = 0 h for the given formula: f(x) = 1/

Algebra ->  Functions -> SOLUTION: <pre>Help! PAGE 131 #19 Find and simplify the difference quotient: f(x + h) - f(x) ----------- -----, h does not = 0 h for the given formula: f(x) = 1/      Log On


   

Question 50737This question is from textbook college algebra: An early functions approach
: 
Help!  PAGE 131 #19
Find and simplify the difference quotient:

 f(x + h) - f(x)
-----------------, h does not = 0
        h
       
for the given formula:

f(x) = 1/x
 This question is from textbook college algebra: An early functions approach

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Help!  PAGE 131 #19
Find and simplify the difference quotient:

 f(x + h) - f(x)
-----------------, h does not = 0
        h
       
for the given formula:

        1
f(x) = ---
        x        
               1
f(x + h) =  -------
             x + h
                     1       1        x - (x + h)     x - x - h         
f(x + h) - f(x) = ------- - ---  =  -------------- = ----------- =  
                   x + h     x         x(x + h)        x(x + h)      

                                                         -h
                                                    ------------
                                                      x(x + h) 



Now divide that by h

 f(x + h) - f(x)         -h         h         -h         1
----------------- = ------------ ÷ --- = ------------ × --- =  
        h             x(x + h)      1      x(x + h)      h

      1
     -h         1
------------ × --- 
  x(x + h)      h
                1

          -1
      ----------
       x(x + h) 

Edwin