Math

1. Given functions , answer the following questions. Show work to support your answer. (3 pts. each)

a. (f o g)(-3)

b. (f o f)(1)

c. (g o f)(x)

d. (g o g )(x)

2. Given . Show work for both a, b and c.

a. Find the domain of f. Show work. (4 pts)

b. Find the x-intercepts of f. Show work. (4 pts)

c. Use a sign test as shown in Section 5.3 to show where the graph of f is above the x-axis and where the graph of f is below the x-axis. (3 pts)

3. Given the equation for the moment of inertia of a rectangular section,, solve for h. Show work. (4 pts)

4. Solve the equation . Show work. (5 pts.)

5. Look at the graphs in exercises #17, #18, #20, #27, #29 on pages 50-52 in Section 1.3.

For each graph, does it represent a one-to-one function? (Yes or No) (no explanation required)

(2 pts. each))

a. #17______ b. #18_______ c. #20______ d. #27______ e. #29_____

6. (4 pts) Given 3x = 24, solve for x. Find an exact answer and a decimal approximation rounded to three decimal places. Show work.

7. (4 pts) Given , solve for x. Find an exact answer and a decimal approximation rounded to three decimal places. Show work.

8a. (2 pts) Write the exponential form of the equation.

8b. (4 pts) Solve for the numerical value of without a calculator. Show work.

9. (8 pts) Use composition of functions to show that

and are inverse functions.

That is, carefully show that and show that . Show work.

10. (5 pts) Find the inverse function of Show work

11. (5 pts) Find the inverse function of Show work

12. Let

(a) (2 pts) The graph of f is transformations of the graph of y = 10 x . Describe the transformations. (Review Section 1.7 Transformations)

(b) (2 pts) What is the domain of f ? Explain your answer.

(b) (4 pts) What is the y-intercept of the graph of f? Show work.

(d) (5 pts) What is the x-intercept of the graph of f? Show work.