By Roger Porkess
The highly-acclaimed MEI sequence of textual content books, aiding OCR's MEI established arithmetic specification, has been up-to-date to check the necessities of the recent requirements, for first instructing in 2004.
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Extra info for A2 Pure Mathematics (C3 and C4)
Make a conjecture about the relationship between the graph of a function and its inverse. You have probably realised by now that the graph of the inverse function is the same shape as that of the function, but reflected in the line y = x. 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.
It could be a translation, a one-way stretch or a reflection. In each case, write down the equation of the image (dashed) in terms of f(x). (ii) (iii) (iv) (v) (vi) C3 3 Exercise 3C (i) 8 The sketch shows the curve with equation y = 2 – 6x – 3x 2 and its axis of symmetry x = –1. y Not to scale O x x = –1 (i) (ii) (iii) (iv) Give the co-ordinates of the vertex and the value of y when x = 0. Find the values of the constants a, b such that 2 – 6x – 3x 2 = a(x + 1)2 + b. Copy the sketch and draw in the reflection of the curve with equation y = 2 – 6x – 3x 2 in the line y = 2.
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 = … .