Composicion de Funciones

Funcion Compuesta: (f o g) (x)
                                (g o f) (x)
                                (f o f) (x)
                               (g o g) (x)

f(x) = (x^2)
g(x) = x-3

1. (f o g) (x) = f (g(x) )
                   = (x-3)^2
                   = (x^2) - 3x - 3x + 9
                   = (x^2) - 6x + 9

2. (g o f) (x) = g (f(x) )
                   = (x^2) - 2

3.(f o g) (x) = f (f(x) )
                  = (x^2)^2
                  = x^4

4.(g o g) (x) = g (g(x) )
                   = x-3-3
                   = x-6

f(x) = (2x^2) - 3x
g(x) = x + 1

1.(f o g)(x) = f (g(x) )
= (2x+1)^2 - 3x-3
= (2x^2)+ 2x + 1) -3x-3
=(2x^2) + 4x + 2 - 3x -3
= (2x^2) + x-1

2. (f o g) (x) = g (f(x) )
= (2x^2) - 3x + 1

3. (f o g) (x) = f (f (x) )
= 2( (2x^2) - 3x)^2) - 3 ( (2x^2) - 3x )

(2x^2)- 3x) ( 2x^2) -3x )
= 4x^4 - 6x^3 + 9x^2
=4x^4 - 12x^3 + 9x^2

2(4x^4 - 12x^3 + 9x^2) - 6x^2 + 9x
8x^4 - 24x^3 + 18x^2 - 6x^2 + 9x
= 8x^4 - 24x^3 + 12x^2 + 9x

4. (f o g) (x) = f (g(x) )

6(X) - 5
  (2)

6X - 5
  2

= 3X - 5