1.1 Functions Inverse Functions Questions - The Answer

1 Gr 12 Maths Functions GR 12 MATHS. Functions . Questions and ANSWERS. Work through the Grade 11 Functions downloads first to ensure your foundation is solid before attempting Inverse Functions . We wish you the best of luck for your exams. From The Answer Series team Copyright The Answer 1. Gr 12 Maths Functions : Questions 2. Consider the function f (x) = - 3x + 6. Is g the Inverse function of f ? Why (not)? (2). Write down the domain and range of f. (a) Name 2 ways in which the domain of f could be Inverse Functions Determine the equation of the Inverse of f in the form (2) restricted to ensure that the Inverse is a function.

2 Sketch the 2 cases. (4). (Gr 12 only) f -1 (x) = .. (2). (b) Determine f -1 (x). in each case. Sketch the 2 cases. Sketch the graphs of the Functions f, f -1 and y = x on Include the line y = x. (4). Questions the same set of axes. What do you notice? (3). (c) Determine the domain and the range of f -1 in each -1 (3). If f (1) = 3, then f = ..? (1). case. (4). f (2) = 0 ( ; ) lies on f and ( ; ) lies on f -1 . (2). 2. 7. Consider the function f where f (x) = - x and x m 0. Concepts and techniques involving the general Write down the coordinates of the x- and y-intercepts of the Write down the domain and range of f.

3 (2). characteristics of Functions (first part of this topic) should be function f (x) = 2x + 6 and of f -1, the Inverse function of f. (4). thoroughly mastered before this section on Inverse Functions . Determine the Inverse function f -1 in the form f -1 (x) = .. (2). In particular, work through Questions 2 7. Sketch the graphs of f and f -1 on the same set of axes, NB: The Inverse of a function REVERSES the process of indicating also the line y = x. (4) Sketch the graphs of the Functions f , f -1 and the line a function.

4 Y = x on the same set of axes. What do you notice? (4). Write down the equation of f -1 in the form f -1 (x) = .. (2). -1. Is f an increasing or a decreasing function? (1). y Are f and f -1 both Functions ? Why (not)? (2). f 1. The graph of f is .. 4. Given : g (x) = 3x - 2. Determine each of the following : Write down the coordinates of the reflections of the 1 following points in the line y = x : O x g - 1 (x) 1 g 1 (6).. -2 g ( x) x P(0; 0), Q(- 1;1), R(2; 4) and S(3; 9). x Let the images be P , Q , R and S respectively.

5 (4). Sketch the graph y = 2 , indicating the coordinates of 2. If the Inverse of f is the reflection of f in the line y = x, Draw a sketch of the graph f which has equation y = x any three points on the graph . (3). then the graph of the Inverse is : for x m 0. (2). Use the three points on the sketch to write down the A. y B. y coordinates of three points on the Inverse function of Which of the points in question lie on the graph of f ? (2). x 2 y=2 . (3) f and its Inverse function, f -1, are reflections in the line.

6 ? (1). 1 O x 2 On the same system of axes, sketch the Inverse function O x x Draw the graph f -1, the Inverse function of f , on the -1 of y = 2 and the line y = x. (3) same system of axes. (2). x Describe the transformation from the graph y = 2 to its Which of the points in question ( question or Answer ). C. y D. y Inverse in words and give the rule for this transformation. (2) lie on the graph of f -1 ? (2). 2 Write down the equation of the Inverse function in the Complete : (a) f (3) = .. O x 1. form x =.

7 O x (b) f -1 (9) = .. -2 1 [ In Topic 4, you will convert this equation to y = .. ] (2). (c) f (2) = 4 ( ; ) lies on f (2) Are both the above graphs Functions ? Why (not)? (2). (d) f -1 (4) =2 ( ; ) lies on f -1 (4). Write down the domain and the range of the graphs of : Consider the graph of f given above. x y (a) y = 2 (b) x = 2 (4) Determine the equation of f -1 in the form f -1 (x) = .. (2). Write down the equation of the given function and of the Inverse function in the form y = .. (2) 2 Is f -1 a function?

8 Give a reason for your Answer . (2). 6. Consider the function f where f (x) = 2x Hence complete: (a) f (x) = .. (b) f -1(x) =.. (2) 2. Write down the domain and range of f. (2) 9. If f (x) = (x + 2) ; x [ - 2, then f -1 (x) is equal to -1 2. Show how the equation of f could have been Sketch the graph of f and g on the same set of axes A. x - 2 B. x -2 C. x-2 D. - x -2 (2). calculated from the equation of f. (2) where g is the reflection of f in the line y = x. Draw the line y = x on the sketch. (3) 10. Given h - 1 (x) = - x.]

9 Then the equation of h is y = .. Explain why f and f -1 are both one-to-one 2 2 2. relations. (2) Determine the equation of g in the form y = .. (2) A. x ; x 0 B. x ; x 0 C. x D. x (2). Copyright The Answer 2. Gr 12 Maths Functions : Questions 11. Given : g (x) = -1 + x. NOTES. Determine the Inverse of g (x) in the form g -1 (x) = .. (4). y 12. f (x) = - 2(x - 3)(x + 1) and D. h (x) = m x + c h E S(2; a). The graphs of f and h have a common x-intercept at Q and f a common y-intercept at E. The turning point of f is at D O x Q.

10 And S(2; a) is a point on f. Calculate the coordinates of E and D. (4). Write down the coordinates of Q. (1). Determine the numerical values of : (a) m (b) a (2)(2). Write down the coordinates of the turning point of f -1 , the Inverse of f. (2). Is f -1 a function? Why (not)? (2). 13. The graph of the function g is shown below. y 6- 4- g 2- O x -4 -2 2 4 6. -2 - -4 - Determine the domain and range of the function. (2). On this set of axes, draw the graph of the Inverse function of g. (4). Explain why this Inverse is a function.