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Further Mathematics Paper 2, Nov/Dec. 2007  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength











Question 9

Two functions f and g are defined on the set R, of real numbers by  f:x® 2x2 - 3x - 5 and g: x ® 3x - 7.

(a) Find g[g(-3)].

(b) For what values of x is g[f(x)] – 8x?

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Observation

Most candidates performed well in this question.  They were able to substitute correctly real numbers to find g[g(- 3)].  The values of g[f(x)]and f[g(x)] were correctly evaluated by most candidates.

            g[g(x)]  = g(3x – 7) = 3(3x – 7) – 7  =  9x  - 28
            \ g[g(-3)] =  - 27 – 28  =   - 55
            g[f(x)] =  g(2x2 – 3x – 5) = 3(2x2 – 3x – 5) – 7 = 6x2 – 9x – 22
            f[g(x)] = f(3x – 7)  =  18x2  - 93x + 114

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