Find the functions f and g and the number c, compute (f o g)(c).?

Question

f(x)= x^2 -2x +1

g(x)=x^2 +2x +1

c=5

Answer 1

First find (fog)(x) [plug g(x) into all the x's in f(x)]:
f(g(x)) = (x^2 + 2x + 1)^2 - 2(x^2 + 2x + 1) + 1

Plug in 5 for x:
f(g(5))
= (5^2 + 2*5 + 1)^2 - 2(5^2 + 2*5 + 1) + 1
= (25 + 10 + 1)^2 - 2(25 + 10 + 1) + 1
= (36)^2 - 2(36) + 1
= 1225

Answer 2

g will be the function that 'fits' inside of the x's in the f(x) function:

(x^2 -2x +1)^2 -2( x^2 -2x +1) +1
and just plug in 5

Answer 3

f(g(5))

g(5) = 25 + 10 + 1 = 36

f(36) = 1225

Answer 4

Well, let's make our lives a little easier: Note that f(x) = (x-1)² and g(x) = (x+1)². Then we have:

(f∘g)(5) = f(g(5)) = f((5+1)²) = f(36) = (36-1)² = 1,225