Section 1.6 Enhanced Assignment

Student: Jalen Wilson Date: 07/11/24 1. Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Assignment: Section 1.6 Enhanced Assignment Determine whether the graph of the function is the graph of a​one-to-one function. 10 y 5 x -10 -5 5 -5 -10 Is the graphed function​one-to-one? No Yes 2. Determine if the function is​one-to-one. ​g(x) = − 7​|x| Is the function​one-to-one? Yes No 10 y 8 6 4 2 -10 -8 -6 -4 -2 -2 -4 -6 -8 -10 x 2 4 6 8 10 10 3. Graph f− 1 ​(x). Identify the domain and range of f− 1 ​(x). Choose the correct graph of f y 1 A. − 2 ≤x≤ ​(x). B. y = f(x) = 0.5 sin x π −1 y π π/ 2 2 − x -1 x − π/ 2 π x π 1 2 -1 C. D. y 1 π/ 2 -1 y 2 − π/ 2 π/ 2 1 y x -1 x 1 − − π/ 2 The domain of f −1 π π 2 2 -1 [ − 0.5,0.5] ​(x) is . (​ Type your answer in interval notation. Type an integer or a​decimal.) The range of f −1 − ​(x) is π π , 2 2 . ​(Type your answer in interval notation. Type an exact​answer, using π as needed. Use integers or fractions for any numbers in the​expression.) 4. The graph of the function f(x) = 8 − 2x​, 0 ≤ x ≤ 4 is shown to the right. Use symmetry with respect to the line y = x to add the graph of f f −1 −1 to the same graph.​(It is not necessary to find a formula for ​.) Identify the domain and range of f −1 y 10 . 5 0 The graph of y = x is shown as a dotted line. Choose the correct graph below. A. B. C. y y y 10 10 f(x) f(x) f 0 −1 0 10 The domain of f −1 −1 is f(x) is f 0 0 [0,8] [0,4] −1 ( x) x 10 f(x) 0 −1 (x) x 0 10 0 f −1 0 . ​(Type your answer in interval​notation.) . ​(Type your answer in interval​notation.) 5. Express as the sum or difference of logarithms. log 3 5x y 10 f (x) x The range of f 10 D. log 3 5x = log 3 5 + log 3 x ​(Simplify your​answer.) (x) x 10 x 0 5 10 6. The graph of the function f is in​blue, and the graph of of the inverse function f −1 2 is in red. The formula for the function f is ​f(x) = x + 1​, x ≥ 0. Find a formula for f −1 f −1 (x) = x−1 ​(Type an exact​answer, using radicals as​needed.) . y 10 8 6 4 2 0 x 0 2 4 6 8 10 −1 7. The formula for a function are y = f(x) and the graphs of f and f given. Find a formula for f −1 6 . y = f(x) 4 5 ​f(x) = x + 3 f −1 y 2 y=f −1 (x) 5 x−3 (​ x) = ​(Type an exact​answer, using radicals as needed.) x -6 -4 -2 2 4 6 -2 -4 -6 3 −1 −1 8. A formula for a function y = ​f(x) is ​f(x) = 5x + 8. Find f (x) and identify the domain and range of f (x). To check the​answer, determine whether f f f −1 −1 (x) = f −1 (f(x)) = x. 3 x−8 (x) = 5 ​(Type an exact​answer, using radicals as needed.) The domain of f −1 (x) is ( − ∞, ∞) . ​(Type your answer in interval​notation.) The range of f −1 (x) is ( − ∞, ∞) . ​(Type your answer in interval​notation.) Does f f −1 (x) = f −1 (f(x)) = x​? No Yes 9. Find the logarithm. log 3 9 log 3 9 = 2 10. ln ( sin θ) − ln sin θ = 3 ​(Type an exact​answer.) sin −1 sin −1 ( − 1) = − π 2 ​(Type an integer or a​fraction.) ( − 1) 12. Express as a single logarithm​and, if​possible, simplify. log 1,000,000 − log 10,000 = log 100 ​(Simplify your​answer.) log 1,000,000 − log 10,000 Find the exact​value, in​radians, of the expression sin a graph of y = sin . 3 ln (3) 11. Find the exact​value, in​radians, of the expression. 13. sin θ Use the properties of logarithms to simplify the expression ln ( sin θ) − ln −1 = −1 1 2 . Use sin −1 2 1 2 ​(Simplify your​answer.) π = 6 x. 14. Find the exact​value, in​radians, of the expression cos Use a graph to help picture the problem. −1 2 2 . cos −1 2 2 = π 4 ​(Type an exact​answer, using π as​needed.)