Chapter 2.1, Problem 62E

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2. Let a, b be real numbers for which b > a. Let functions f, g, h be defined on a domain [a, b] in the following manner. when x = a; a+b 2 when x = a; f(x) = g(x) = h(x) = (x – a)(x – b). when x > a. when x > a. x-a (a) Sketch a graph of functions f, g, h. (b) Function h is continuous at every point in its domain, but functions f, g are not continuous at x = a. Explain. (c) Function ƒ does not have a maximum value. Explain. (d) Function does not have a minimum value. Explain. (e) Function h attains both a maximum value and a minimum value. The maximum value occurs at the points x = a and x = b; and the minimum value occurs at the point x = a+b 말. Explain.

5. If f(x)=-3x+5 a) Find f-¹(x). b) Use function composition to prove that they are inverse functions. c) Graph f(x) and tell me why it is a one-to-one function.

2. Let f(x)=x2x3 - 3. a) Find the domain of the function: ○ [-3,00) Ⓒ (-∞0, 3] (-∞0, 3) U (3, 0) (∞, -3) U (-3,00) b) Find the range of the function: (-∞0, 2) U (2,00) ○ [2,00) Ⓒ (-∞, -2] O (-∞, -2) U (-2, 0) c) Is f a one-to-one function? Yes, f is one-to-one. No, f is not one-to-one. d) Use your answer from part c to determine if the inverse of the function f is a function. Yes, the inverse of the function f is a function. No, the inverse of the function f is not a function.