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Math 112 Quiz
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 xaxis.(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
yaxis, we get y = f(−x + 1). So move left 1 unit, then reflect over
the yaxis.
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 onetoone (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.
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