By Roger Porkess
The highly-acclaimed MEI sequence of textual content books, assisting OCR's MEI dependent arithmetic specification, has been up to date to compare the necessities of the recent requisites, for first instructing in 2004.
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Additional info for A2 Pure Mathematics (C3 and C4)
Similarly g 3(x) means three applications of g. In order to apply a function repeatedly its domain and co-domain must be the same. Order of functions If f is the rule ‘square the input value’ and g is the rule ‘add 1’, then x So f ⎯→ square x2 g ⎯→ add 1 x 2 + 1. gf(x) = x 2 + 1. 37 Notice that gf(x) is not the same as fg(x), since for fg(x) you must apply g first. In the example above, this would give: C3 3 Functions x g ⎯→ add 1 (x + 1) f ⎯→ square (x + 1)2 and so fg(x) = (x + 1)2. Clearly this is not the same result.
5 has no solution π (i) for 0 р θ р – (ii) for any value of θ? 2 EXERCISE 3D 1 The functions f, g and h are defined by f(x) = x 3, g(x) = 2x and h(x) = x + 2. Find each of the following, in terms of x. 2 gf fgh (viii) (fh)2 (ii) (iii) (iv) (v) (vi) fh ghf h2 (ix) Exercise 3D fg hf (vii) g2 (i) C3 3 Find the inverses of the following functions. f(x) = 2x + 7 (ii) f(x) = 4 – x 4 (iii) f(x) = –––– (iv) f(x) = x 2 – 3 x у 0 2–x The function f is defined by f(x) = (x – 2)2 + 3 for x у 2. (i) 3 (i) (ii) 4 Sketch the graph of f(x).
2 gf fgh (viii) (fh)2 (ii) (iii) (iv) (v) (vi) fh ghf h2 (ix) Exercise 3D fg hf (vii) g2 (i) C3 3 Find the inverses of the following functions. f(x) = 2x + 7 (ii) f(x) = 4 – x 4 (iii) f(x) = –––– (iv) f(x) = x 2 – 3 x у 0 2–x The function f is defined by f(x) = (x – 2)2 + 3 for x у 2. (i) 3 (i) (ii) 4 Sketch the graph of f(x). On the same axes, sketch the graph of f –1(x) without finding its equation. Express the following in terms of the functions f: x → g: x → x + 4. (i) x→ x+4 (ii) x →x + 8 (iii) x→ x+8 (iv) x→ x and x+4 5 The functions f, g and h are defined by 3 h(x) = 2 – x.