Maths Assignment ...Help me Please !!!!!

Hi, here is my maths assignment any help would be great,im so confused with this!!!(Doh)

1. Let** A = **{ 4, 5, 6, 7 } and **B** = {11, 12, 13, 14, 15,1 6 } and

let us define binary relations S and T as follows:

**(a)** For all (x, y) є A x B, (x, y) є S ↔x divides y (3 marks)

**(b)** For all (x, y) є A x B, (x, y) є T ↔ 2x > y(3 marks)

By drawing mapping diagrams for each relation determine:

(i) the type of mapping

(ii) which of the above relations if any between **A** and **B** forms a

function.

2. Let **R **be the relation between { 5, 6, 7 } and given by { 8, 9, 10, 11 }

**R = **{ (5, 8), (5, 10), (6, 9), (6, 10), (7, 11) }

Let **S **be the relation between { 8, 9, 10, 11 } and given by { 5, 6, 7 }

**S = **{ (8, 6), (8, 5), (9, 5), (9, 7), (10, 7) }

Calculate: **(a) (i)** **R-1 **(1 mark)

**(ii)** **S-1 **(1 mark)

**(iii) S º R **(2 marks)

**(b)** Verify that **(S º R)-1** = **R-1 ° S-1 **(3 marks)

3. The functions f and g are defined by

f: x → x2 + 7 , x є **R**

g: x → 3x + 3 , x є **R**

h: x → __1__ , x ≠ 0, x є **R**

x

(a) Find the inverses of functions f, g and h (3 marks)

(b) Hence find:

(i) fo g (x) (ii) h-1og (x) (2 marks)

(c) Evaluate:

(i) f (3) (ii) fo g (3) (2 marks)

4. The function f is defined by f(x) = __x + 2__ , x є **R**

** 3**

(a) Find f-1(x) (1 mark)

(b) Given that g(x) = x2, x є **R**, find an expression for f-1og (x) (1 mark)

(c) Solve the equation f-1og(x) = 25 (3 marks)

5. (a) Evaluate the following:

(i) 38 (ii) 25-1/2 (2 marks)

(b) Simplify the following leaving your answers in index form.

(i) e6. e2 (ii) __818__

84 (2 marks)

6. (a) Convert the number 345 into:

(i) binary

(ii) hexadecimal numbers (4 marks)

(b) Convert the following numbers to decimal numbers:

(i) 1111112 (ii) 2978 (4 marks)

7. (a) Draw by hand on graph paper, the graphs of

y = 2e-*x* and y = *x* + 1 for -2 ≤ *x* ≤ 2

(3 marks)

(b) Hence solve the equation 2e-*x* - *x * = 1

(2 marks)

8. (a) Simplify the following expressions into a single logarithmic term.

(i) log 7 + log 6 – log 3

(ii) log 5t - log 3t

(4 marks)

(b) Solve the following equations, giving your answers to 2 decimal places:

(i) 10*x * = 17 (ii) ln (1 + 3*x*) = 2.25

(4 marks)