Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following.
1. f(g(-1)) 2. f o h(3) 3. g(f(-5))
4. h(f(x)) 5. f(f(x)) 6. h o g(x)
II. Let f(x) = 9 – x , g(x) = x2 + 4, and h(x) = x – 2. Compute the following:
7. g(f(12)) 8. f(g(2)) 9. h(f(x))
III. Let g(x) = 4x + 1 represent the conversion from spots to stars. Let h(x) = x2 - 2
represent the conversion from stars to asteroids. Create a composite function that converts
spots directly to asteroids.
IV. Let k(x) = x - 1 represent the conversion from toes to moles. Let p(x) = 2x + 3
represent the conversion from moles to rolls. Create a composite function that converts toes
directly to rolls.
I'd appreciate the help. If you don't want to give me answers, please teach me how to do them.

Respuesta :

4. Since f(x) = 2x - 1, we are looking for h(2x - 1), which is (2x-1)^2 + 1. By tha time you expand this you'll get, 4x^2 - 4x + 2. So that is the answer.
5. f(f(x))  = f(2x - 1) = 2(2x - 1) - 1 = 4x - 3
6. h(g(x)) = h(3x) = (3x)^2 + 1 = 9x^2 + 1