+ All Categories
Home > Education > Question bank for functions IB HL and SL Maths

Question bank for functions IB HL and SL Maths

Date post: 18-Jan-2017
Category:
Upload: dr-anil-khare
View: 2,389 times
Download: 216 times
Share this document with a friend
21
IB Questionbank Maths SL 1 1. Given that f (x) = 2e 3x , find the inverse function f 1 (x). Working: Answer: ....................................................................... (Total 4 marks) 2. Two functions f and g are defined as follows: f (x) = cos x, 0 x 2; g (x) = 2x + 1, x . Solve the equation (g f)(x) = 0. Working: Answer: ...................................................................... (Total 4 marks)
Transcript
  • IB Questionbank Maths SL 1

    1. Given that f (x) = 2e3x

    , find the inverse function f 1

    (x).

    Working:

    Answer:

    .......................................................................

    (Total 4 marks)

    2. Two functions f and g are defined as follows:

    f (x) = cos x, 0 x 2;

    g (x) = 2x + 1, x .

    Solve the equation (g f)(x) = 0.

    Working:

    Answer:

    ......................................................................

    (Total 4 marks)

  • IB Questionbank Maths SL 2

    3. The diagram shows three graphs.

    y

    x

    B

    A

    C

    A is part of the graph of y = x.

    B is part of the graph of y = 2x.

    C is the reflection of graph B in line A.

    Write down

    (a) the equation of C in the form y =f (x);

    (b) the coordinates of the point where C cuts the x-axis.

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 4 marks)

  • IB Questionbank Maths SL 3

    4. Let f(x) = 7 2x and g(x) = x + 3.

    (a) Find (g f)(x).

    (2)

    (b) Write down g1

    (x). (1)

    (c) Find (f g1

    )(5).

    (2)

    (Total 5 marks)

    5. Two functions f, g are defined as follows:

    f : x 3x + 5

    g : x 2(1 x)

    Find

    (a) f 1

    (2);

    (b) (g f )(4).

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 4 marks)

  • IB Questionbank Maths SL 4

    6. Let f (x) = 2x, and g (x) =

    2x

    x, (x 2).

    Find

    (a) (g f ) (3);

    (b) g1

    (5).

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 6 marks)

  • IB Questionbank Maths SL 5

    7. Consider the functions f : x 4(x 1) and g : x 2

    6 x.

    (a) Find g1

    .

    (b) Solve the equation ( f g1

    ) (x) = 4.

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 6 marks)

  • IB Questionbank Maths SL 6

    8. Let f (x) = 2x + 1 and g (x) = 3x2 4.

    Find

    (a) f 1

    (x);

    (b) (g f ) (2);

    (c) ( f g) (x).

    Working:

    Answers:

    (a) ..

    (b) ..

    (c) .. (Total 6 marks)

  • IB Questionbank Maths SL 7

    9. The function f is given by f (x) = x2 6x + 13, for x 3.

    (a) Write f (x) in the form (x a)2 + b.

    (b) Find the inverse function f 1

    .

    (c) State the domain of f 1

    .

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (c) ..................................................................

    (Total 6 marks)

  • IB Questionbank Maths SL 8

    10. (a) The diagram shows part of the graph of the function f (x) = . px

    q The curve passes

    through the point A (3, 10). The line (CD) is an asymptote.

    15

    10

    5

    -5

    -10

    -15

    C

    A

    D

    y

    x15105051015

    Find the value of

    (i) p;

    (ii) q.

  • IB Questionbank Maths SL 9

    (b) The graph of f (x) is transformed as shown in the following diagram. The point A is

    transformed to A (3, 10).

    y

    x

    15

    15

    10

    10

    5

    50

    5

    5

    10

    10

    15

    15

    A

    C

    D

  • IB Questionbank Maths SL 10

    Give a full geometric description of the transformation.

    Working:

    Answers:

    (a) (i) ...........................................................

    (ii) ...........................................................

    (b) ..................................................................

    ..................................................................

    (Total 6 marks)

    11. Let f (x) = ex

    , and g (x) = x

    x

    1, x 1. Find

    (a) f 1

    (x);

    (b) (g f ) (x).

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 6 marks)

  • IB Questionbank Maths SL 11

    12. Let f (x) = x3 4 and g (x) = 2x.

    (a) Find (g f ) (2).

    (b) Find f 1

    (x). (Total 6 marks)

    13. Consider the functions f (x) = 2x and g (x) = 3

    1

    x, x 3.

    (a) Calculate (f g) (4).

    (b) Find g1

    (x).

    (c) Write down the domain of g1

    .

    Answers:

    Working:

    (a) .....................................................

    (b) .....................................................

    (c) ..................................................... (Total 6 marks)

  • IB Questionbank Maths SL 12

    14. The function f is defined by ,9

    3)(

    2xxf for 3 < x < 3.

    (a) On the grid below, sketch the graph of f.

    (b) Write down the equation of each vertical asymptote.

    (c) Write down the range of the function f. (Total 6 marks)

  • IB Questionbank Maths SL 13

    15. The function f is given by f (x) = e(x11)

    8.

    (a) Find f 1

    (x).

    (b) Write down the domain of f l

    (x).

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 6 marks)

    -

    16. Let f (x) = ln (x + 2), x 2 and g (x) =

    e(x4)

    , x 0.

    (a) Write down the x-intercept of the

    graph of f.

    (b) (i) Write down f (1.999).

    (ii) Find the range of f.

    (c) Find the coordinates of the point of

    intersection of the graphs of f and

    g. (Total 6 marks)

  • IB Questionbank Maths SL 14

    Working:

    Answers:

    (a) ..................................................................

    (b) ..................................................................

    (Total 6 marks)

    17. Let g (x) = 3x 2, h (x) = 4

    5

    x

    x, x 4.

    (a) Find an expression for (h g) (x). Simplify your answer.

    (b) Solve the equation (h g) (x) = 0. (Total 6 marks)

    18. The functions f (x) and g (x) are defined by f (x) = ex and g (x) = ln (1+ 2x).

    (a) Write down f 1

    (x).

    (b) (i) Find ( f g) (x).

    (ii) Find ( f g)1

    (x). (Total 6 marks)

  • IB Questionbank Maths SL 15

    19. Let f (x) = 22

    3

    qx

    xp

    , where p, q

    +.

    Part of the graph of f, including the asymptotes, is shown below.

    (a) The equations of the asymptotes are x =1, x = 1, y = 2. Write down the value of

    (i) p;

    (ii) q. (2)

    (b) Let R be the region bounded by the graph of f, the x-axis, and the y-axis.

    (i) Find the negative x-intercept of f.

    (ii) Hence find the volume obtained when R is revolved through 360 about the x-axis. (7)

    (c) (i) Show that f (x) =

    222

    1

    13

    x

    x.

    (ii) Hence, show that there are no maximum or minimum points on the graph of f. (8)

  • IB Questionbank Maths SL 16

    (d) Let g (x) = f (x). Let A be the area of the region enclosed by the graph of g and the

    x-axis, between x = 0 and x = a, where a 0. Given that A = 2, find the value of a. (7)

    (Total 24 marks)

    20. Let f (x) = 4x , x 4 and g (x) = x2, x .

    (a) Find (g f ) (3).

    (b) Find f 1

    (x).

    (c) Write down the domain of f 1

    . (Total 6 marks)

    21. The functions f and g are defined by f : x 3x, g : x x + 2.

    (a) Find an expression for (f g)(x).

    (2)

    (b) Find f1

    (18) + g1

    (18). (4)

    (Total 6 marks)

  • IB Questionbank Maths SL 17

    22. The function f is defined by f(x) = 29

    3

    x, for 3 < x < 3.

    (a) On the grid below, sketch the graph of f.

    (2)

    (b) Write down the equation of each vertical asymptote. (2)

    (c) Write down the range of the function f. (2)

    (Total 6 marks)

    23. Consider f(x) = 5x .

    (a) Find

    (i) f(11);

    (ii) f(86);

    (iii) f(5). (3)

  • IB Questionbank Maths SL 18

    (b) Find the values of x for which f is undefined. (2)

    (c) Let g(x) = x2. Find (g f)(x).

    (2)

    (Total 7 marks)

    24. Let f (x) = ln (x + 5) + ln 2, for x 5.

    (a) Find f 1

    (x). (4)

    Let g (x) = ex.

    (b) Find (g f) (x), giving your answer in the form ax + b, where a, b, . (3)

    (Total 7 marks)

    25. Let f(x) = 3x, g(x) = 2x 5 and h(x) = (f g)(x).

    (a) Find h(x). (2)

    (b) Find h1

    (x). (3)

    (Total 5 marks)

  • IB Questionbank Maths SL 19

    26. Let f be the function given by f(x) = e0.5x

    , 0 x 3.5. The diagram shows the graph of f.

    (a) On the same diagram, sketch the graph of f1

    . (3)

    (b) Write down the range of f1

    . (1)

    (c) Find f1

    (x). (3)

    (Total 7 marks)

    27. Let f(x) = k log2 x.

    (a) Given that f1

    (1) = 8, find the value of k. (3)

  • IB Questionbank Maths SL 20

    (b) Find f1

    3

    2.

    (4)

    (Total 7 marks)

    28. Let f(x) = log3 x , for x > 0.

    (a) Show that f1

    (x) = 32x

    . (2)

    (b) Write down the range of f1

    . (1)

    Let g(x) = log3 x, for x > 0.

    (c) Find the value of (f 1

    g)(2), giving your answer as an integer.

    (4)

    (Total 7 marks)

    29. Let f(x) = cos 2x and g(x) = 2x2 1.

    (a) Find

    2

    f .

    (2)

    (b) Find (g f)

    2

    .

    (2)

    (c) Given that (g f)(x) can be written as cos (kx), find the value of k, k .

    (3)

    (Total 7 marks)

  • IB Questionbank Maths SL 21

    30. Let f(x) = 2x3 + 3 and g(x) = e

    3x 2.

    (a) (i) Find g(0).

    (ii) Find (f g)(0).

    (5)

    (b) Find f1

    (x). (3)

    (Total 8 marks)

    31. Let f(x) = x2 and g(x) = 2x 3.

    (a) Find g1

    (x). (2)

    (b) Find (f g)(4).

    (3)

    (Total 5 marks)


Recommended