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Find the requested composite function value.


For the given functions f and g, find the requested composite function value.

f(x) = x-6/x  , g(x) = x2 + 9;
Find (g f)(-2).
 
Please step by step instructions. Thanks ;-)

Comments

Bella, you have to use parentheses to avoid double reading

f(x) = (x - 6) / x   or   f(x) = x - (6/x)

and special sign " ^ " to indicate the exponent

g(x) = x^2 + 9
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2 Answers

What you're going to do first is put the f function into the g function. You do this by replacing any x in g with the f equation:
 
g(x )= (x-6/x)2 + 9
 
Now you replace the x with the -2 and simplify it:
 
((2)-6/(2))2 + 9
(2-3)2 + 9
(-1)2 + 9
-2 + 9
=7
 
 

Comments

As I understood the functions are 

           x - 6
f(x) = ---------
              x

g(x) = x2 + 9 


(g ° f)(- 2) ?

                    x - 6
(g ° f)(x) = (-------)2 + 9    
                      x

                      - 2 - 6
(g ° f)(- 2) = (----------)2 + 9 = 25
                          - 2


OR

                   6
f(x) = x  −  ----
                   x

g(x) = x2 + 9  


                           6
(g ° f)(x) = ( x − ----) 2 + 9 
                           x

                               6
(g ° f)(- 2) = (- 2 − ----) 2 + 9   
                             - 2

(g ° f)(- 2) = (- 2 + 3)2 + 9 = 10