Math 112 - Fall 2008

Complete each of the following problems. Show all work. Make sure to clearly
label your answer. Any work that is crossed out will not be assessed. Any
incorrect work will be assessed. Make sure that all work is legible.

1. Vital Errors
(a) Factor and simplify completely:

(b) Rewrite without negative exponents , factor, and simplify:

2. Describe in words the correct order of translations and reflections necessary
to get the graph of each of the following equations from y = f(x):

(a) y = −f(x)
Reflect over the x-axis.(b) y = f(1 − x)
This is the same as y = f(−x+1). So if we take y = f(x) and move
it to the left 1, we get y = f(x + 1). Then if we reflect over the
y-axis, we get y = f(−x + 1). So move left 1 unit, then reflect over
the y-axis.

3. Consider the functions

(a) Find the domain of f.
For the domain of f, we want all values x which make the quantity
under the radical be non -negative. So x − 4 ≥ 0. So x ≥ 4, making
the domain be [4,∞).

(b) Find (fg)(x).

4. Consider the functions

(a) Find (f ο g)(x).

(b) Find (g ο f)(x).

(c) Are these functions inverses? Explain.
These function are NOT inverses, for a variety of reasons. To list a
couple:
(i) The function g(x) is not one-to-one (it’ s a parabola )
(ii) (fοg)(x) ≠ x, which it would necessarily need to be in order
for these two functions to be inverses of one another.