Find the requested composite function value.

Question

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 ;-)

Answer 1

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

 

 

Answer 2

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