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find (f o g)(x)

 

 Oct 6, 2020
 #1
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(f o g)(x)   =   f( g(x) )

                                         Since  g(x) = -x + 1,  we can substitute  -x + 1  in for  g(x)

(f o g)(x)   =   f( -x + 1 )

                                         And  f(x) = x2 + 2, so to find  f(-x + 1), plug  -x + 1  into

                                         the function by replacing every instance of  x  with  -x + 1

(f o g)(x)   =   (-x + 1)2 + 2

                                                        Expand the squared term by multiplying it out.

(f o g)(x)   =   (-x + 1)(-x + 1) + 2

 

(f o g)(x)   =   x2 - 2x + 1 + 2

 

(f o g)(x)   =   x2 - 2x + 3

 

smileysmiley

 Oct 6, 2020

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