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

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)