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    Need some help on functions in P2 please...This question is Number 2 from June 2003 Paper (edexcel)

    f: x -> x^2 - 2x + 3 0 less the or eqal to x wich is less then or equal to 4
    g : x -> ax^2 + 1 where a is a constant

    a) Find the range of f
    b) given that gf(2) = 16 find the value of a.

    a) i thort taht u shud only put in f(0) and f(4) into the equation but that ent right....y not? how do u work it out..

    b) firstly u put in f(2) into x^2 - 2x =3 and get f(x) = 3
    then i thort u use the f(x) = 3 and put that into ax^2 = 1 to get 3^2a + 1 = 16....but that isnt right either..help plsss
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    (Original post by ladoooo)
    Need some help on functions in P2 please...This question is Number 2 from June 2003 Paper (edexcel)

    f: x -> x^2 - 2x + 3 0 less the or eqal to x wich is less then or equal to 4
    g : x -> ax^2 + 1 where a is a constant

    a) Find the range of f
    b) given that gf(2) = 16 find the value of a.

    a) i thort taht u shud only put in f(0) and f(4) into the equation but that ent right....y not? how do u work it out..

    b) firstly u put in f(2) into x^2 - 2x =3 and get f(x) = 3
    then i thort u use the f(x) = 3 and put that into ax^2 = 1 to get 3^2a + 1 = 16....but that isnt right either..help plsss
    You should really post your maths queries now in the maths sub-forum, at the top of this page. You'll get answered a lot faster.

    a)
    f(x) = x² - 2x + 3, 0 <= x <= 4
    g(x) = ax² + 1, a const


    I don't know if P2 covers max and min of functions, but if it does this is how.

    f'(x) = 2x - 2
    at f'(x) = 0
    2x - 2 = 0
    x = 1
    ===
    This is a minimum (obvious since you have a quadratic/parabola)

    f(x=1) = 1² -2.1 + 3
    f(1) = 2
    fmin = 2
    ======

    To find the max,

    f(0) = 0 - 0 + 3
    f(0) = 0, end of range of x
    =====

    f(4) = 4² - 2.4 + 3
    f(4) = 11, top of range of x
    ======

    so, by comparing results,

    fmax = 11
    ======

    range of f is
    2 <= f <= 11
    =========

    b)
    g(f(x)) = a(x² - 2x + 3)² + 1
    g(f(2)) = a(2² - 2.2 + 3)² + 1
    g(f(2)) = a(3)² + 1
    g(f(2)) = 9a + 1

    then,

    9a + 1 = 16
    9a = 15
    a = 5/3
    =====

    That looks like what you would have gotten!
    What's the answer then?
 
 
 
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