Question

Dadas as funções reais de variável real f(x)= x + 3 e g(x)= X² - 5, determinar:
a) (gof)(x)
b) (fog)(x)
c) f(f(x))
d)g(g(x)

Answer 1

a ) 

(gof)=g(f(x))
(gof)=g(x+3)
(gof)=(x+3)²-5
(gof)=x²+6x+4

b )

(fog)(x)=f(g(x))
(fog)(x)=f(x²-5)
(fog)(x)=x²-5+3
(fog)(x)=x²-2

c ) f(f(x))=(fof)(x)
f(f(x))=f(x+3)
f(f(fx))=x+3+3
f(f(x))=x+6

d )  
g(g(x))=(gog)(x)
g(g(x))=(x²-5)²-5
g(g(x))=x^4-10x²+20