Ejercicios adicionales de función compuesta

EJERCICIOS ADICIONALES DE FUNCIÓN COMPUESTA:

1  HALLAR FOG(X) Y GOF(X):

F(x)= 7x+2                                        G(x)= ×-4

Dom f(x)= R                                      Dom g(x)= R

·         FOG(x)= f(g(x))

            = 7(x-4)+2

                          = 7x-28+2

                          = 7x-26

·         GOF(x)= g(f(x))

            =  (7x+2)-4

            =  7x-2

2         HALLA FOG(X) Y GOF(X):

F(x)= x² +8x+4                           G(x)= x+6

Dom f(x)= [-2;4]                       Dom g(x)= [-5;8]

·         Dom fog(x)= {x/x € dom g(x) ^ g(x) € dom f(x)}

                       x€ [-5;8] ^ x+6€ [-2;4]

                        -5<x<8 ^ -2<x+6<4

                       -5<x<8 ^  -8<x<-2

Dominio (FoG)(x): <-5;-2> 

·            FOG(x)= f(g(x))

            = (x+6)2+8(x+6)+4

            = x²+36+8x+48+4

            = x²+8x+88

·         GOF(X)= g(f(x))

            = (x²+8x+4)+4

            = x²+8x+8

            =  7x-2

3         HALLA FOG(X) Y GOF(X):

F(x)= 2x-5                           G(x)= x+1

Dom f(x)= R                        Dom g(x) R

·         FOG(x)= f(g(x))             

            = 2(x+1)-5

            = 2x+2-5

            = 2x-3

·         GOF(x)= g(f(x))

            = (2x-5)+1

            = 2x-4