Math 135
Functions: Arithmetic
Worksheet
Compute and simplify:
(x)
1. f (x) = x2 + x + 1, f (x+h)−f
=
h
=
2. g(x) = x2 + 4x + 4, g(b)−g(a)
b−a
3. f (x) = x2 , g(x) = x3 + 1, h(x) =
1
x
(a) f (g(x))
(b) g ◦ f (x)
(c) h(f (2))
(d) f ◦ g ◦ h(2)
(e) f ◦ h(g(x))
√
4. f (x) = 3x + 1, g(x) = 3x + 1, h(x) =
1
x2
(a) x3 f · h(x)
(b) (g(x))2
(c)
h
(x)
g
(d) g · (h(x) ◦ f (x))
(e)
h
(x)
g
◦ (g ◦ h(x))
Sample Midterm
30 A B C D
University of Hawai‘i at Mānoa
82
Sample Final
R Spring - 2014