Math 1010-2 Final Practice 3:
Other techniques
1. Suppose f (x) =
x−4
and g(x) = 2x + 1
x2 − 3x
(a) What is the natural domain of f ?
(b) Find f (5).
(c) Find (f ◦ g)(x).
2. Find the inverse function of
f (x) = ln(2x + 1)
What are the domains of f and f −1 , respectively?
3. Factor the following polynomial:
x4 − 5x2 + 4
4. Find the quotient and the remainder if 5x3 + x2 − 3x + 1 is divided by x2 − 2x + 1
5. Find the quotient and the remainder if 5x3 + x2 − 3x + 1 is divided by x + 1
6. Complete the square in the following trinomial:
2x2 + 6x + 1
7. An auto store sells a pair of car mats for $16 during a sale. The discount rate is 20%. What is the
original price of the car mats?
8. It takes you 6 hours to dig a hole. It takes your brother 8 hours to dig the same hole. Your younger
sister takes 12 hours. How long does it take the three of you working together?
9. Iodine-131 has a half life of 7 days. If you start with 16 milligrams of Iodine-131, how much will
left after 21 days?