University:
University of Vermont
Course:
MATH 1034 | Pre-Calculus Mathematics
Academic year:

2024
Views:

199

Pages:

2
Author:

Mercedes Bishop

PAL Worksheet 6 √ √ √ x−1 1. Let f (x) = x2 + 2x − 3, g(x) = 3 x, h(x) = x2 + 4, j(x) = and k(x) = (x + 3 x)2 . x+1 Identify each of the following functions as a composition of some of these functions. √ a. l(x) = 3 x2 + 2x − 3 √ √ b. m(x) = (3 x)2 + 2(3 x) − 3 √ x2 + 4 − 1 c. n(x) = √ x2 + 4 + 1 √ d. p(x) = (x2 + 2x − 3 + 3 x2 + 2x − 3)2 √ e. q(x) = 3 4 x2 + 4 p f. r(x) = (x2 + 2x − 3)2 + 4 r x−1 g. s(x) = 3 x+1 h. t(x) = x2 + 2x − 4 x2 + 2x − 2 2. The graph of an invertible function f is shown. Sketch the graph of of the inverse function f −1 . f −1 f 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 -12-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 -12-11-10-9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 1 2 3 4 5 6 7 8 9 10 11 12 3. Verify that f and g are inverses by using composition. That is, show that (f ◦ g)(x) = x and (g ◦ f )(x) = x. x−3 a. f (x) = 6x + 3 and g(x) = . 6 √ b. f = x5 + 3 and g(x) = 5 x − 3. √ c. f (x) = 3 x + 2 and g(x) = (x − 2)3 . 2x + 1 x+1 d. f (x) = , x 6= 1 and g(x) = , x 6= 2. x−1 x−2 4. Each of the following functions has an inverse. Algebraically determine the rule for the inverse function. Express your answer using the proper notation for the inverse function. a. f (x) = 7x3 + 4 √ b. g(x) = 5 4x − 3 √ c. h(x) = 4 + 3 5x − 3 1 d. u(x) = 2x − 9 5x + 1 e. v(x) = 3 − 2x x f. k(x) = 6 + 3x − 2