Square Root and Quadratic Function Problem: Let f and g be defined by where the values

Chapter 1, Problem 6

(choose chapter or problem)

Square Root and Quadratic Function Problem: Let f and g be defined by where the values of x make f(x) a real number g(x) = x2 4 where x is any real number a. Plot the graphs of f, g, and f g on the same screen. Use a friendly x-window of about 10 x 10 that includes the integers as grid points. Sketch the result. b. Find the domain of f g . Explain why the domain of f g has positive and negative numbers, whereas the domain of f has only positive numbers. c. Show algebraically that f(g(4)) is defined, but f(g(1)) is undefined. d. Show algebraically that g(f(6)) is defined, but g(f(3)) is undefined. e. Plot the graph of g f. Make sure that the window has negative and positive y-values. f. The graph of g f appears to be a straight line. By finding an equation for g(f(x)) explicitly in terms of x, determine whether this is true.