Functions please help

Question

Let f (x) = 3x2 – 5x + 9 and g(x) = 1 – 4x. (a) Find the difference (f – g)(x) and simplify the results. Show work. (b) Find the composite function (f o g)(x) and simplify the results. Show work.

Answer 1

f(x ) = 3X^2 - 5X + 9      g(x) = 1 - 4x

 

a) (  f - g ) ( x ) = 3X^2 - 5X + 9 - ( 1 - 4x ) =

 

                        =  3 X^2 - 5X + 9 -1 + 4X

                     

                         = 3 X^2 - X + 8

 

b)

      ( f ° g ) (x) = 3 ( 1 -4x ) ^2 - 5 ( 1 - 4X) + 9

 

                        =  3 ( 1 - 8X + 16 X^2 ) - 5 + 20X + 9

 

                         = 48 X^2 - 4X +7