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    C3 Chapter2 FunctionsQuestions

    Uploaded by

    Willie Salim
    This document contains past exam questions related to functions. It includes questions testing skills such as finding inverse functions, composition of functions, solving equations involving functions, determining domains and ranges, and sketching graphs of functions. The questions cover a range of topics and difficulty levels involving defining, evaluating, composing, inverting and graphing various functions.

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    © All Rights Reserved
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    C3 Chapter2 FunctionsQuestions

    Uploaded by

    Willie Salim
    135 views9 pages
    This document contains past exam questions related to functions. It includes questions testing skills such as finding inverse functions, composition of functions, solving equations involving functions, determining domains and ranges, and sketching graphs of functions. The questions cover a range of topics and difficulty levels involving defining, evaluating, composing, inverting and graphing various functions.

    Original Description:

    klk

    Original Title

    C3 Chapter2 FunctionsQuestions (1)

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    This document contains past exam questions related to functions. It includes questions testing skills such as finding inverse functions, composition of functions, solving equations involving functions, determining domains and ranges, and sketching graphs of functions. The questions cover a range of topics and difficulty levels involving defining, evaluating, composing, inverting and graphing various functions.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    135 views9 pages

    C3 Chapter2 FunctionsQuestions

    Uploaded by

    Willie Salim
    This document contains past exam questions related to functions. It includes questions testing skills such as finding inverse functions, composition of functions, solving equations involving functions, determining domains and ranges, and sketching graphs of functions. The questions cover a range of topics and difficulty levels involving defining, evaluating, composing, inverting and graphing various functions.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 9
    At a glance
    Powered by AI
    The document describes various types of functions including linear, logarithmic and exponential functions. It also provides examples of operations that can be performed on functions such as composition, evaluation and finding inverse functions.

    The document describes linear, logarithmic and exponential functions. It also discusses inverse functions.

    Some examples of operations performed on functions in the document include composition (fg), evaluation (f(x)), and finding inverse functions (f^-1).

    C3 – Chapter 2 – Functions Exam Questions

    [June 2013] 7. The function f has domain –2 ≤ x ≤ 6 and is linear from (–2, 10) to (2, 0) and
    from (2, 0) to (6, 4). A sketch of the graph of y = f(x) is shown in Figure 1.

    (a) Write down the range of f.


    (1)
    (b) Find ff(0).
    (2)

    The function g is defined by

    4  3x
    g: x , x  ℝ, x ≠ 5.
    5 x

    (c) Find g–1(x).


    (3)
    (d) Solve the equation gf(x) = 16.
    (5)

    [June 2013 (R)] 4. The functions f and g are defined by

    f: x 2 x 3, x

    g: x 3  4x , x

    (a) State the range of f. (2)


    (b) Find fg(1). (2)
    (c) Find g–1, the inverse function of g. (2)
    (d) Solve the equation

    gg(x) + [g(x)]2 = 0
    (5)
    [June 2012] 6. The functions f and g are defined by

    f: x  ex + 2, x  ℝ,

    g : x  ln x, x > 0.

    (a) State the range of f.


    (1)
    (b) Find fg(x), giving your answer in its simplest form.
    (2)
    (c) Find the exact value of x for which f(2x + 3) = 6.
    (4)
    (d) Find f −1, the inverse function of f, stating its domain.
    (3)
    (e) On the same axes sketch the curves with equation y = f(x) and y = f−1(x), giving the
    coordinates of all the points where the curves cross the axes.
    (4)

    [Jan 2012] 7. The function f is defined by

    3( x  1) 1 1
    f:x  – , x ℝ, x > .
    2x  7x  4 x  4
    2
    2

    1
    (a) Show that f(x) = .
    2x  1
    (4)
    (b) Find f −1(x).
    (3)
    (c) Find the domain of f −1.
    (1)

    g(x) = ln (x + 1).

    1
    (d) Find the solution of fg(x) = , giving your answer in terms of e.
    7
    (4)
    [June 2011] 4. The function f is defined by

    f : x  4 − ln (x + 2), x  ℝ, x  –1.

    (a) Find f −1(x).


    (3)
    (b) Find the domain of f −1.
    (1)
    The function g is defined by

    x  ℝ.
    2
    g : x  e x − 2,

    (c) Find fg(x), giving your answer in its simplest form. (3)
    (d) Find the range of fg. (1)

    [Jan 2011] 6. The function f is defined by


    3  2x
    f: x  , x  ℝ, x ≠ 5.
    x5

    (a) Find f−1(x). (3)

    Figure 2
    The function g has domain –1  x  8, and is linear from (–1, –9) to (2, 0) and from (2, 0) to
    (8, 4). Figure 2 shows a sketch of the graph of y = g(x).

    (b) Write down the range of g. (1)


    (c) Find gg(2). (2)
    (d) Find fg(8). (2)
    (e) On separate diagrams, sketch the graph with equation

    (i) y = g(x),
    (ii) y = g−1(x).

    Show on each sketch the coordinates of each point at which the graph meets or cuts the
    axes. (4)
    (f) State the domain of the inverse function g−1.
    (1)
    [June 2010] 4. The function f is defined by

    f : x |→ |2x − 5|, x  ℝ.

    (a) Sketch the graph with equation y = f(x), showing the coordinates of the points where the
    graph cuts or meets the axes.
    (2)
    (b) Solve f(x) =15 + x.
    (3)

    The function g is defined by

    g : x |→ x2 – 4x + 1, x  ℝ, 0 ≤ x ≤ 5.

    (c) Find fg(2).


    (2)
    (d) Find the range of g.
    (3)

    [Jan 2010] 9. (i) Find the exact solutions to the equations

    (a) ln (3x – 7) = 5,
    (3)
    (b) 3x e7x + 2 = 15.
    (5)

    (ii) The functions f and g are defined by

    f (x) = e2x + 3, x ∈ ℝ,

    g(x) = ln (x – 1), x ∈ ℝ, x > 1.

    (a) Find f –1 and state its domain.


    (4)
    (b) Find fg and state its range.
    (3)
    ANSWERS
    [June 2013] 7.

    [June 2013 (R)] 4.


    [June 2012] 6.
    [Jan 2012] 7.

    [June 2011] 4.
    [Jan 2011] 6.

    [June 2010] 4.
    [Jan 2010] 9.

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