Download A2 Pure Mathematics (C3 and C4) by Roger Porkess PDF

By Roger Porkess

The highly-acclaimed MEI sequence of textual content books, helping OCR's MEI based arithmetic specification, has been up-to-date to check the necessities of the recent requisites, for first instructing in 2004.

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Write down the values of (a) f(0) (b) f(7) (c) f(–3). A function is defined by g:(polygons) ⎯→ (number of sides). What are (a) g(triangle) (b) g(pentagon) (c) g(decagon)? The function t maps Celsius temperatures on to Fahrenheit temperatures. 9C It is defined by t: C ⎯→ –– + 32. Find 5 (a) t(0) (b) t(28) (c) t(–10) (d) the value of C when t(C) = C. Find the range of each of the following functions. ) (vi) f(x) = 2 – 3x f(i) = sin i y = x2 + 2 y = tan i f : x ⎯→ 3x – 5 f : x ⎯→ 2x (vii) y = cos x (i) (ii) (iii) (iv) (v) (viii) (ix) (x) 5 f : x ⎯→ x 3 – 4 1 f(x) = –––––2 1+x f(x) = x –3+3 xу0 0° р i р 180° x ∈ {0, 1, 2, 3, 4} 0° Ͻ i Ͻ 90° x ∈‫ޒ‬ x ∈ {–1, 0, 1, 2} π π –– рxр– 2 2 x∈‫ޒ‬ x∈‫ޒ‬ xу3 The mapping f is defined by f(x) = x 2 0 р x р 3 f(x) = 3x 3 р x р 10.

To see why this is so, think of a function f(x) mapping a on to b; (a, b) is clearly a point on the graph of f(x). The inverse function f –1(x), maps b on to a and so (b, a) is a point on the graph of f –1(x). The point (b, a) is the reflection of the point (a, b) in the line y = x. 20. This result can be used to obtain a sketch of the inverse function without having to find its equation, provided that the sketch of the original function uses the same scale on both axes. 20 Finding the algebraic form of the inverse function To find the algebraic form of the inverse of a function f(x), you should start by changing notation and writing it in the form y = … .

The language of functions A mapping is any rule which associates two sets of items. In this example, each of the names on the left is an object, or input, and each of the reasons on the right is an image, or output. For a mapping to make sense or to have any practical application, the inputs and outputs must each form a natural collection or set. The set of possible inputs (in this case, all of the people who flew to Geneva from London in January) is called the domain of the mapping. The set of possible outputs (in this case, the set of all possible reasons for flying to Geneva) is called the co-domain of the mapping.

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