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

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By Roger Porkess

The highly-acclaimed MEI sequence of textual content books, aiding OCR's MEI dependent arithmetic specification, has been up-to-date to compare the necessities of the hot requirements, for first instructing in 2004.

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Sample text

The curve passes through the origin and has a maximum point at (1, 1). Functions C3 3 Sketch, on separate diagrams, the graphs of (i) y = f(x) + 2 (ii) y = f(x + 2) (iii) y = f(2x) giving the co-ordinates of the maximum point in each case. [UCLES] Composite functions It is possible to combine functions in several different ways, and you have already met some of these. For example, if f(x) = x 2 and g(x) = 2x, then you could write f(x) + g(x) = x 2 + 2x. In this example, two functions are added.

F :x→x+2 x ∈ ‫ޚ‬. Inverse function: f –1: x → x – 2 x ∈ ‫ޚ‬. Function: For a mapping to be a function which also has an inverse function, every object in the domain must have one and only one image in the co-domain, and vice versa. This can only be the case if the mapping is one-to-one. So the condition for a function f to have an inverse function is that, over the given domain and co-domain, f represents a one-to-one mapping. This is a common situation, and many inverse functions are self-evident as in the following examples, for all of which the domain and co-domain are the real numbers.

Given that Exercise 3E f(x) = x 2 f(x) = 2 – x C3 3 0рxϽ1 1 р x Ͻ 2, sketch the graph of f(x) for –2 р x Ͻ 4. 32 shows the parts of the line and the curve which define f(x). These parts span an interval of length 2 (the period of the function) and thus form the basic repeating pattern. The second diagram shows this pattern repeated three times in the interval –2 р x Ͻ 4. EXERCISE 3E 1 For each of the following curves, say whether the function is odd, even or neither. (i) (ii) (ii) (iii) (iii) 53 (iv) (iv) (v) (v) (vi) (vi) Functions C3 3 2 For each of the following functions, say whether it is odd, even, periodic, or any combination of these.