Question

Hola disculpa como puedo resolver composición de funciones.

f(x) = x/x+1
g(y)= x+4

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

Answer 1

Respuesta:

(f o f)(x) = f(f(x))
(f o f)(x) = f(x) / (f(x) + 1)
(f o f)(x) = (x / (x + 1)) / (x / (x + 1) + 1)
(f o f)(x) = (x / (x + 1)) / ((x + (x + 1)) / (x + 1))
(f o f)(x) = (x / (x + 1)) / ((x + 2) / (x + 1))
(f o f)(x) = (x) / (x + 2) 
(f o f)(x) = x / (x + 2) 

(f o g)(x) = f(g(x)) 
(f o g)(x) = g(x) / (g(x) + 1)
(f o g)(x) = (x + 4) / ((x + 4)+ 1)
(f o g)(x) = (x + 4) / (x + 5)

(g o f)(x) = g(f(x))
(g o f)(x) = f(x) + 4
(g o f)(x) = x / (x + 1) + 4
(g o f)(x) = (x + 4(x + 1)) / (x + 1)
(g o f)(x) = (x + 4x + 4) / (x + 1)
(g o f)(x) = (5x + 4) / (x + 1)

(g o g)(x) = g(g(x))
(g o g)(x) = g(x) + 4
(g o g)(x) = x + 4 + 4
(g o g)(x) = x + 8