due in an hour

Instruction:

1. Do it yourself. You should not seek help from others, nor through internet. You cannot help others either.

2. It is an open book exam.

3. No need to copy the problems. Just write your name, number of problem, and the answer of the problem in an answer sheet.

4. Show your work. Most of the problems are not trivial. Wrong answers without detail will have 0 points.

1. (1 pt) If f(x) = x2 – 2x + 4, evaluate the difference quotient

f(a + h) – f(a)

         h

 

2. (4 pts) Find the domain and range of the function. Write your answer in interval notation.

(a) f(x) =     3__   

                2x – 1

                   _______

(b) g(x) = √(16 – x4)

(c) h(x) = x2 + 6x + 9

(d) f(x) = 3 + sin 2t

3. (3 pts) Use transformations to sketch the graph of the function. Start from the graph of the corresponding basic function. You must show all the transformations.

y = – (x – 2)3 + 4

4. (1 pt) Graph the function.

               –x + 1       if x < 0  

f(x) = {2x – 1 if x ≥ 0 

5. (4 pts) If f(x) = 1 / x and g(x) = x2 – 9, find the functions and their domains.

(a) f ◦ g

(b) g ◦ f

(c) f ◦ f

(d) g ◦ g

                                                                        ________

6. (1 pt) Express the function F(x) = 1 / √(x + √(x))  as a composition of three functions.

7. (1 pt) If f(x) = x / π + sin x, find f -1(1).

8. (1 pt) Find the inverse function of f(x) = (x + 2) / (2x – 1).

9. (4 pts) Simplify each expression.

(a) 2x2(3x5)2

(b) (2x-2)-3 x-3

(c) 3a3/2 a1/2 / a-1

(d) (a1/2 b1/2) / (ab)1/2

10. (2 pts) Solve each equation for x.

(a) 4x = 23x

(b) tan x = 1

11. (4 pts) Determine whether f is even, odd, or neither.

(a) f(x) = |x| + 1

(b) f(x) = x3 – 1 

(c) f(x) = –sin x

(d) f(x) = cos 2x

12. (4 pts) If f(x) = 2x + 1 and g(x) = 1 – √(x), find

(a) (f + g) (x) and its domain

(b) (f – g) (x) and its domain

(c) (f ∙ g) (x) and its domain

(d) (f / g) (x) and its domain