Let f be the linear function in blue and let g be the parabo

Let f be the linear function (in blue) and let g be the parabolic function (in red) below. Evaluate the following: (f g)(2)= (g f)(2)= (f f)(2)= (g g)(2)= (f + g)(4)= (f/g)(2)= Enter \"DNE\" if an answer does not exist.

Solution

1) (f o g)(2) = f(g(2))

==> f(0)

==> -2

Hence (f o g)(2) = -2

2) (g o f)(2) = g(f(2))

==> g(0)

==> 4

Hence (g o f)(2) = 4

3) (f o f)(2) = f(f(2))

==> f(0)

==> -2

Hence (f o f)(2) = -2

4) (g o g)(2) = g(g(2))

==> g(0)

==> 4

Hence (g o g)(2) = 4

5) (f + g)(4)

==> f(4) + g(4)

==> 2 + 4 = 6

Hence (f + g)(4) = 6

6) (f/g)(2) = f(2) / g(2)

==> 0/0

==> DNE

Hence (f/g)(2) = DNE