Question

Given: f(a)= a³ +a and g(a) = a -1 Find: (fog)(a)​

Answer 1

Answer:

(fog)(a)​ = a³ - 3a² + 4a - 2

           = (a - 1)×(a² - 2a + 2)

Step-by-step explanation:

Given :

g(a) = a -1 

f(a)= a³ +a

…………………………

(fog)(a)​ = f(g(a)​))

           = g(a)³ + g(a)

           = (a - 1)³ + (a - 1)

           = (a³ - 3a² + 3a - 1) + (a - 1)

           = a³ - 3a² + 3a - 1 + a - 1

           = a³ - 3a² + 3a + a - 1 - 1

           = a³ - 3a² + 4a - 2

Second method :

(fog)(a)​ = f(g(a)​))

           = f(a - 1)

           = (a - 1)³ + (a - 1)

           = (a - 1)×[(a - 1)² + 1]

           = (a - 1)×[a² - 2a + 1 + 1]

           = (a - 1)×(a² - 2a + 2)