I am stuck on this problem

Question

Let f(x) = (x − 2)2 and g(x) = x + 9,
and find the following.

 

(a) (f?g)(−9)


(b) (g?f)(−9)

Answer 1

Hi Corina,

 

If the question you are asking is about composition functions with the notation f o g

 

Let f(x) = (x − 2)² and g(x) = x + 9,
and find the following.

(a) (fog)(−9) =f(g(-9))        g(-9)=-9+9       f(0)=  (0-2)²

                                                = 0                 = 4                     

 

                                          Therefore, (fog)(-9)= f(g(-9))=4


(b) (gof)(−9)=g(f(-9))         f(-9) = (-9-2)²         g( 121)=  121  +9

                                                = (-11)²                     = 130

                                                = 121

                                                                                                

                                      Therefore, (gof)(-9)=g(f(-9))=130

 

Hope this helps you understand the process.