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Math Help - Maths Assignment ...Help me Please !!!!!

  1. #1
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    Maths Assignment ...Help me Please !!!!!

    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 R (2 marks)


    (b) Verify that (S 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)





    (Total Marks = 50)
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  2. #2
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    Quote Originally Posted by chris89108 View Post
    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 R (2 marks)


    (b) Verify that (S 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)






    (Total Marks = 50)
    It is MHF policy to not knowingly help with assignments that count towards a student's final grade. Such assignments are meant to be the student's own work, not the work of others.
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