3. f(g(x)) f(x) = x 2 g(x) (g(x)) 2 x g(x) = x + 1 x x+1 (x+1) 2
4.
5. f x x f x ( ) ( ) ( ) ? = + Þ ¢ = 1 2 f x x x x ( ) ( ) = + = + + 1 2 1 2 2 Þ ¢ = + f x x ( ) 2 2 f x x f x ( ) ( ) ( ) ? = + Þ ¢ = 3 2 f x x x x ( ) ( ) = + = + + 3 6 9 2 2 Þ ¢ = + f x x ( ) 2 6 = + 2 1 ( ) x = + 2 3 ( ) x
6. f x x f x x ( ) ( ) ( ) ( ) = + Þ ¢ = + 1 2 1 2 f x x f x ( ) ( ) ( ) = + Þ ¢ = 7 2 f x x f x x ( ) ( ) ( ) ( ) = + Þ ¢ = + 3 2 3 2 2 7 ( ) x + f x x x x f x x x ( ) ( ) ( ) ( ) = + = + + Þ ¢ = + = + 7 14 7 2 14 2 7 2 2
7. f x x f x ( ) ( ) ( ) = + Þ ¢ = 2 3 2 2 2 3 ( ) x + 2 5 2 ( ) x + f x x x x x x f x x x ( ) ( ) ( )( ) ( ) ( ) = + = + + = + + Þ ¢ = + = + 2 3 2 3 2 3 4 12 9 8 12 4 2 3 2 2 Oops f x x x x f x x x ( ) ( ) ( ) ( ) = + = + + Þ ¢ = + = + 5 2 25 20 4 50 40 10 5 2 2 2 Oops again = + 2 2 2 3 . ( ) x = + 5 2 5 2 . ( ) x f x x f x ( ) ( ) ( ) = + Þ ¢ = 5 2 2
8. f x x f x ( ) ( ) ( ) = + Þ ¢ = 7 3 2 7 2 7 3 . ( ) x + f x x x x f x x x x ( ) ( ) ( ) ( ) . ( ) = + = + + Þ ¢ = + = + = + 7 3 49 42 9 98 42 14 7 3 7 2 7 3 2 2 f x x f x ( ) ( ) ( ) = + Þ ¢ = 2 1 3 2 3 2 1 2 . ( ) x + f x x x x x f x x x x x x x ( ) ( ) ( ) ( ) ( ) . ( ) = + = + + + Þ ¢ = + + = + + = + = + 2 1 8 12 6 1 24 24 6 6 4 4 1 6 2 1 2 3 2 1 3 3 2 2 2 2 2
9. f x x ( ) ( ) = + 2 2 1 f x x x x f x x x ( ) ( ) ( ) = + = + + Þ ¢ = + 2 2 4 2 3 1 2 1 4 4 = + = + 4 1 2 2 1 2 2 x x x x ( ) . ( )