For fx 2 x and g x 3x2 x 9 find the following functions

For f(x) = 2 - x and g (x) = 3x^2 + x + 9, find the following functions. a. (f compositefunction g)(x); b. (g compositefunction f)(x); c. (f compositefunction g)(3); d. (g compositefunction f)(3) a. (f compositefunction g)(x) = b. (g compositefunction f)(x) = (f compositefunction g)(3) = d. (g compositefunction f)(3) =

Solution

f(x) = 2-x ; g(x) = 3x^2 + x+9

a) ( fog)(x) :

f(g(x)) = 2 - (3x^2 + x +9) = -3x^2 - x- 7

b) (g of)(x) :

g(f(x)) = 3(2- x)^2 + 2 -x +9 = 3(x^2 +4 - 4x) +2-x +9

= 3x^2 +12 - 12x +2 -x +9

= 3x^2 -13x + 23

c) (f o g)(3) = -3(3)^2 - 3- 7 = -27 - 10 = -37

d) ( g o f)(3) = 3(3)^2 -13(3) + 23

= 27 - 39 +23

= 11