نویسنده : امیر انصاری

1. $$
   f(g(0))
   $$
   
2. $$
   g(f(0))
   $$
   
3. $$
   f(g(x))
   $$
   
4. $$
   g(f(x))
   $$
   
5. $$
   f(f(-5))
   $$
   
6. $$
   g(g(2))
   $$
   
7. $$
   f(f(x))
   $$
   
8. $$
   g(g(x))
   $$
   

پاسخ

1. $$
   f(g(0)) = f((0)^2 - 3) = f(0-3) = f(-3) = (-3) + 5 = 2
   $$
   
2. $$
   g(f(0)) = g( 0+5 ) = g(5) = 5^2 - 3 = 25-3=22
   $$
   
3. $$
   f(g(x)) = f(x^2 - 3) = (x^2-3) + 5 = x^2 -3 + 5 = x^2 +2
   $$
   
4. $$
   g(f(x)) = g(x+5) = (x+5)^2 -3 = x^2 +10x + 25 - 3 = x^2 + 10x + 22
   $$
   
5. $$
   f(f(-5)) = f( (-5) + 5 )=f(0) = 0+5=5
   $$
   
6. $$
   g(g(2)) = g( 2^2 - 3 ) = g(4-3) = g(1) = 1^2 - 3 = 1-3 = -2
   $$
   
7. $$
   f(f(x)) = f( x+5 ) = (x+5)+5 = x+5+5 = x+10
   $$
   
8. $$
   g(g(x)) = g ( x^2 - 3) = (x^2-3)^2 - 3 = x^4 - 6x^2 + 9 - 3 = x^4 - 6x^2 + 6
   $$