ind (g°w)(x)and (w°g)(x)for g(x)=2x-2 and w(x)=x2-2x+2 (g°w)(x)= Switch to Equation Editor (w°g)(x)=

Question

ind (g°w)(x)and (w°g)(x)for g(x)=2x−2 and w(x)=x^2−2x+2
(g°w)(x)=
(w°g)(x)=

Answer 1

g(x) = 2x - 2

w(x) = x² - 2x + 2

 

 

(g°w)(x) =

g(w(x)) =

g(x² - 2x + 2) =

2(x² - 2x + 2) - 2 =

2x² - 4x

 

Simplify.

 

2x(x - 2)

 

 

(w°g)(x)=

w(g(x)) =

w(2x - 2) =

(2x - 2)² - 2(2x - 2) + 2 =

4x² - 8x + 4 - 4x + 4 + 2 =

4x² - 12x + 10

 

Simplify.

 

2(2x² - 6x + 5) =

2(2x - 5)(x - 1)