Cambridge Additional Mathematics

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62 Functions (Chapter 2)

2 Given f(x)=x^2 +3, find:

a f(¡3) b xsuch that f(x)=4.

3 Solve forx:

a j 1 ¡ 2 xj=11 b j 5 x¡ 1 j=j 9 x¡ 13 j

4 Draw a sign diagram for each graph:

ab

5 Given h(x)=7¡ 3 x, find:

a h(2x¡1) b h^2 (x) c h^2 (¡1)

6 Suppose the range of y=f(x) is fy:¡ 76 y 6 ¡ 3 g. Write down the range of y=jf(x)j.

7 Draw the graph of y=

̄

̄ 1 ¡^1

3 x

̄

̄.

8 Suppose f(x)=1¡ 2 x and g(x)=5x.

a Find in simplest form: i fg(x) ii gf(x).

b Solve fg(x)=g(x+2).

9 Suppose f(x)=ax^2 +bx+c, f(0) = 5, f(¡2) = 21, and f(3) =¡ 4. Finda,b, andc.

10 If y=f(x) has an inverse, sketch the graph of y=f¡^1 (x):

abc

11 Find the inverse function f¡^1 (x) for:

a f(x)=7¡ 4 x b f(x)=

3+2x

5

12 Given f:x 7! 5 x¡ 2 and h:x 7!

3 x

4

, show that (f¡^1 ±h¡^1 )(x)=(h±f)¡^1 (x).

13 Given f(x)=2x+11 and g(x)=x^2 , find (g±f¡^1 )(3).

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_02\062CamAdd_02.cdr Thursday, 3 April 2014 4:10:09 PM BRIAN