Question

Due date: 16 March 2021 before 11.00 PM 1. Find the inverse function (if it is defined) of the following functions. (4 marks) a. f(x) = (2x-3)/(x+5) (x in R, x ? -5) b. f(x) = x" + 2. (x in R) 2. Three different functions, f(x), g(x) and h(x), have the same graph on [0, 2] as shown in Figure. On separate diagrams, sketch their graphs for [-4, 4] given that a. f(x) is periodic with period 2; b. g(x) is periodic with period 4 and is even; c. h(x) is periodic with period 4 and is odd. (6 marks) 3. Calculate the rate of change of the linear functions given by (2 marks) a. f(x) = 1/2 x - 4 b. f(2) = 5 and f(-3) = 10 4. Determine which of the following quadratic functions are irreducible (show your working) (3 marks) a. f(x) = x" + 3x + 4 b. f(x) = 4x" - 12x + 9 c. f(x) = 9 - 5x - 2x" 5. For what values of x are the values of the quadratic function below greater than zero? (2 marks) a. f(x) = x" - 3x - 6 6. Show that the roots ?, ? of the equation x" + 4x + 1 = 0 satisfy the equations. (8 marks) ?" + ?" = 14 ?³ + ?³ = -52 Hence find the quadratic equations whose roots are a. ?" and ?" b. ?³ and ?³ 7. Express as partial fractions. (6 marks) (a) (x + 2) / ((x - 1)(x - 4)) (b) (x" + 4) / ((x + 1)(x - 3)) (c) (x" - 2x + 3) / ((x + 2)"(x - 1)) 8. Sketch the graph of the function given below locating asymptotes (4 marks) y = (x" - 8x + 15) / x 9. Plot the curve whose parametric equations are x = t(t + 4), y = t + 1. Show that it is a parabola. (5 marks) 10. Sketch for -3? ? x ? 3?. (4 marks) a. y = sin 2x b. y = cos 1/2 x 11. Solve the following equations for 0 ? x ? 2?. (6 marks) a. 3sin"x + 2sinx - 1 = 0 (b) 4cos"x + 5cosx + 1 = 0 (c) 2tan"x - tanx - 1 = 0 12. Express as a single logarithm: (1 mark) 4 ln 3 - 1/2 ln 36 13. Sketch carefully the graphs of the functions (4 marks) (a) y = 2^x, y = log?x (on the same axes) (b) y = e^x, y = ln x (on the same axes)

          Due date: 16 March 2021 before 11.00 PM

1. Find the inverse function (if it is defined) of the following functions. (4 marks)
a. f(x) = (2x-3)/(x+5) (x in R, x ? -5)
b. f(x) = x" + 2. (x in R)
2. Three different functions, f(x), g(x) and h(x), have the same graph on [0, 2] as shown in Figure. On separate diagrams, sketch their graphs for [-4, 4] given that
a. f(x) is periodic with period 2;
b. g(x) is periodic with period 4 and is even;
c. h(x) is periodic with period 4 and is odd. (6 marks)
3. Calculate the rate of change of the linear functions given by (2 marks)
a. f(x) = 1/2 x - 4
b. f(2) = 5 and f(-3) = 10
4. Determine which of the following quadratic functions are irreducible (show your working) (3 marks)
a. f(x) = x" + 3x + 4
b. f(x) = 4x" - 12x + 9
c. f(x) = 9 - 5x - 2x"
5. For what values of x are the values of the quadratic function below greater than zero? (2 marks)
a. f(x) = x" - 3x - 6
6. Show that the roots ?, ? of the equation x" + 4x + 1 = 0 satisfy the equations. (8 marks)
?" + ?" = 14
?³ + ?³ = -52
Hence find the quadratic equations whose roots are
a. ?" and ?"
b. ?³ and ?³
7. Express as partial fractions. (6 marks)
(a) (x + 2) / ((x - 1)(x - 4))
(b) (x" + 4) / ((x + 1)(x - 3))
(c) (x" - 2x + 3) / ((x + 2)"(x - 1))
8. Sketch the graph of the function given below locating asymptotes (4 marks)
y = (x" - 8x + 15) / x
9. Plot the curve whose parametric equations are x = t(t + 4), y = t + 1. Show that it is a parabola. (5 marks)
10. Sketch for -3? ? x ? 3?. (4 marks)
a. y = sin 2x
b. y = cos 1/2 x
11. Solve the following equations for 0 ? x ? 2?. (6 marks)
a. 3sin"x + 2sinx - 1 = 0
(b) 4cos"x + 5cosx + 1 = 0
(c) 2tan"x - tanx - 1 = 0
12. Express as a single logarithm: (1 mark)
4 ln 3 - 1/2 ln 36
13. Sketch carefully the graphs of the functions (4 marks)
(a) y = 2^x, y = log?x (on the same axes)
(b) y = e^x, y = ln x (on the same axes)

$Due date: 16 March 2021 before 11.00 PM 1. Find the inverse function (if it is defined) of the following functions. (4 marks) a. f(x) = (2x-3)/(x+5) (x in R, x ? -5) b. f(x) = x" + 2. (x in R) 2. Three different functions, f(x), g(x) and h(x), have the same graph on [0, 2] as shown in Figure. On separate diagrams, sketch their graphs for [-4, 4] given that a. f(x) is periodic with period 2; b. g(x) is periodic with period 4 and is even; c. h(x) is periodic with period 4 and is odd. (6 marks) 3. Calculate the rate of change of the linear functions given by (2 marks) a. f(x) = 1/2 x - 4 b. f(2) = 5 and f(-3) = 10 4. Determine which of the following quadratic functions are irreducible (show your working) (3 marks) a. f(x) = x" + 3x + 4 b. f(x) = 4x" - 12x + 9 c. f(x) = 9 - 5x - 2x" 5. For what values of x are the values of the quadratic function below greater than zero? (2 marks) a. f(x) = x" - 3x - 6 6. Show that the roots ?, ? of the equation x" + 4x + 1 = 0 satisfy the equations. (8 marks) ?" + ?" = 14 ?³ + ?³ = -52 Hence find the quadratic equations whose roots are a. ?" and ?" b. ?³ and ?³ 7. Express as partial fractions. (6 marks) (a) (x + 2) / ((x - 1)(x - 4)) (b) (x" + 4) / ((x + 1)(x - 3)) (c) (x" - 2x + 3) / ((x + 2)"(x - 1)) 8. Sketch the graph of the function given below locating asymptotes (4 marks) y = (x" - 8x + 15) / x 9. Plot the curve whose parametric equations are x = t(t + 4), y = t + 1. Show that it is a parabola. (5 marks) 10. Sketch for -3? ? x ? 3?. (4 marks) a. y = sin 2x b. y = cos 1/2 x 11. Solve the following equations for 0 ? x ? 2?. (6 marks) a. 3sin"x + 2sinx - 1 = 0 (b) 4cos"x + 5cosx + 1 = 0 (c) 2tan"x - tanx - 1 = 0 12. Express as a single logarithm: (1 mark) 4 ln 3 - 1/2 ln 36 13. Sketch carefully the graphs of the functions (4 marks) (a) y = 2^x, y = log?x (on the same axes) (b) y = e^x, y = ln x (on the same axes)$

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