Funciones Compuestas

1. Escriba la funcion P(x)= (x+2)5 como una función compuesta (g o f).
P(x)= (x+2)5
(g o f)= (x+2)5
g(x)= x5
f(x)= (x+2)
(gof)= g(f(x))
= (x+2)
= (x+2)5
Escriba la función p(x)= x=x2+4como una función compuesta ( g o f).
P(x)= x=x2+4
(g o f)= x=x2+4
g(x)= x2
f(x)= +4
(gof)= g(f(x))
= 4
= x2+4

2. Dadas las funciones:

fx=x-32

g(x)=x
a) (g o f)(x)= g(f(x))
=x-32
=x = x ( x-32 )
=x-32

b) (fog) (x)= f(g(x))
=x
=x-32=x-32 (x )

=x-32
(g o f)(x)= (f o g) (x)
Dadas las funciones:
fx=6xx2-9

g(x)=3x
a) (f o g)(x)= g(f(x))
= 6xx2-9
=3x =3x ( 6xx2-9 )
=3x( 6x )x2-9

b) (g o f) (x)
=3x
= 6xx2-9= 6xx2-9 (3x )

=3x( 6x )x2-9
(g o f)(x)= (f o g) (x)

Dadas las funciones:
fx=x2-5x+3
g(x)=x2
a) (g o f)(x)= g(f(x))=x2-5x+3
=x2= x2 (x2-5x+3 )
= x4-5x3+3x2

b) (f o g) (x)= f(g(x))
=x2
=x2-5x+3
=x2-5x+3 ( x2 )
= x4-5x3+3x2

(g o f)(x)= (f o g) (x)

Dadas las funciones:
fx=2x2+5x
gx=4-7x
a) (g of)(x)= g(f(x))
=2x2+5x
=4-7x= 4-7x ( 2x2+5x )
= 8x2+20-14x3-35x

b) (f o g) (x)= f(g(x))
=4-7x
=2x2+5x =2x2+5x (4-7x )
= 8x2+20-14x3-35x

(g o f)(x)= (f o g) (x)

Dadas las funciones:fx=3x2+2

g(x)=13x2+2
a) (g o f)(x)= g(f(x))
= 3x2+2
=13x2+2 = 13x2+2 (3x2+2 )
=1

b) (f o g) (x)
= 1 3x2+2
= 3x2+2 = 3x2+2 (1 3x2+2 )
=1
(g o f)(x)= (f o g) (x)

Dadas lasfunciones:
fx=2x+1

gx=x2-3

h(x)=x-52
a) (f o g) (x)= f (g(x))
= x2-3
=( 2x+1 )2-3
= 4x2+4x-2
b) (g o f) ( x)= g(f(x))
= 2x+1
= 2x+1(x2-3)
=( 2x+1 )2-3
= 4x2+4x-2
c) (f oh)(x)= f(h(x))
= x-52
=x-52 ( 2x+1 )
= x-5 ( 2x+1 )2
= 2x2-9x-52
d) (h o f) (x)= h(f(x))
= 2x+1
=( 2x+1 )x-52
=( 2x+1 )x-5 2
=2x2-9x-52

e) (g o h) ( x)= g(f(x))
= = x-52
= x-52(x2-3)=x-5 (x2-3) 2
= x3-5x2-3x-15
f) (g o h) ( x)= g(f(x))
= (x2-3)
= (x2-3) x-52
=x-5 (x2-3) 2
= x3-5x2-3x-15

(g o f o h) (x)= (g o f ) (h(x))
= (g o f ) ( x-52 )
= 4x-52 2 +4x-52 2-2...