Chapter 8.1, Problem 9QR

Number 16

Give the domain for g(x)=x+4/x^2−9x+20 in interval notation.   __________

Let f(x) = x4 - 2x2.  Find the intervals on which f is increasing and decreasing, and give the coordinates of the turning points

PLEASE HELP ANSWER THIS QUESTION, VERY VERY URGENT

Find the inverse of x^2-20x   and find the domain

Give the domain of the following function in interval notation.   t(x) =             1                        64 + x^2

Consider the function: g(z) = with the domain IR\{8} (i.e. all real numbers except 8) and the image R\{1} (i.e. all real numbers I+10 except 1). Find the expression for the inverse function g(r). Select one: O not in the list O (10+8x)/(x-1) O 10+8x O (10+8x)/(x+1) O (x-8)/(x+10)

Suppose f(x) = x² + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in the interval [-4,-1]. (a) First, we show that f has a root in the interval (-4,-1). Since f is a choose function on the interval [-4, -1] and f(-4)= and f(-1) =, the graph of y = f(x) must cross the x-axis at some point in the interval (-4,-1) by the ◆. Thus, f has at least choose one root in the interval [—4, -1]. (b) Second, we show that f cannot have more than one root in the interval [−4, -1] by a thought experiment. Suppose that there were two roots x = a and x = b in the interval [-4, −1] with a < b. Then f(a) = f(b) = Since fis choose on the interval [-4,-1] and choose on the interval (-4,-1), by choose there would exist a point c in interval (a, b) so that f'(c) = 0. However, the only solution to f'(x) = 0 is x = not in the interval (a, b), or in [−4, -1]. Thus, f cannot have more than one root in [−4, −1]. 0 which is

Suppose that f has a domain of [5, 13] and a range of [6, 16]. (a) What are the domain and range of the function y = f(x) + 2? (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol ∞ for infinity and the appropriate type of parenthesis "(", ")", "[", or "]" depending on whether the interval is open or closed.) D= R =