**E.8**

27. Show that each function is the inverse of the other: f(x) = 4x - 7 and
.

**Answer:** Yes, the functions are inverse of each other. f(g(x)) = x and g(f(x)) =
x.

28. Find the inverse of the function .

**Answer:** f^{ -1}(x) = x^{2} + 1 for x ≥ 0

29. Does the graph below represent a function that has inverse function?

**Answer:** No, notice that horizontal lines can be drawn and
intersect the graph more than once.

30. The formula is used to convert from x degrees Celsius to y degrees Fahrenheit.

Find the formula to convert from y degrees Fahrenheit to x degrees Celsius. Show
that this formula

is the inverse function of f(x).

**Answer:** is the inverse, then
, therefore the

formula is the inverse of f(x).

**E.9
**

31. Graph the polynomial function: f(x) = 2x

x-intercepts, state whether the graph crosses the x-axis or touches the x-axis, indicate the y-intercepts.

If necessary, find a few additional points and graph the function.

x-axis at every zero since each zero has multiplicity 1.

32. Graph the rational function
. Indicate all x-intercepts, y-intercepts, horizontal asymp-

tote, vertical asymptote(s). If necessary, find a few additional points and graph
the function.

**Answer:** x = 0, y = 0, vertical asymptote at x = 2, horizontal asymptote at y =
3.

33. Sketch the graph of the exponential function
:

**Answer: **Horizontal asymptote located at y = -3

34. Graph the following Piecewise function and state the
domain, range and intervals where the func-

tion is increasing, decreasing and constant.

**Answer:** The domain of this function is the set of all Real
Numbers, the range is the interval

[1,∞). The interval of increasing is (1,∞), the interval of decreasing is (-∞,-1) and the interval

where the function is constant is (-1, 1). See the graph below.

**E.10
**

35. Apply properties of Logarithms to simplify each expression.

36. Expand each expression by writing in terms of sum or difference of logarithms.

37. Write the expression as a single Logarithm.

38. Write the expression as a single Logarithm.

**Answer:**

**E.11**

39. Suppose that y is such that . Evaluate

**Answer:**

40. Solve for all the values of x that satisfy the equation:
.

**Answer:**

41. Solve the equation by making an appropriate substitution,
.

**Answer:**

42. Solve the radical equation. Check the proposed solutions.
.

**Answer: **x = 10

43. Find the rational zeros of f. List any irrational zero correct to two
decimal places.

f(x) = x^{4} + 5x^{3} - 3x^{2} - 35x - 28.

Answer: Rational zeros: , Irrational zeros:

44. Solve the exponential equation. Round your answer to four decimal places.

**Answer:** x = -37.2754

45. Solve the radical equation. Check the proposed solutions.

**Answer: **x = 2, note that x = 14 does not satisfy the original equation.

46. Solve the exponential equation .

**Answer:** y = -1.