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) 10x = 17 (ii) ln (1 + 3x) = 2.25
(4 marks)
