1 Function Enrichment PDF August 14 2009

7/29/2019 1 Function Enrichment PDF August 14 2009

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FUNCTIONS

http://mathsmozac.blogspot.com Page 1


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1. Given that mxxf +4: and4

3:

1 + nxxf , find the values of m and n.

Answer:- m = 3 ; n =1

4

2. Given that 12: xxf , xxg 4: and baxxfg +: , find the values ofa and b .Answer:- a = 8 ; b = 1

3. Given that 3: +xxf , 2: bxaxg + and 56366: 2 ++ xxxgf , find thevalues ofa and b .

Answer:- a = 2 ; b = 6

4. Given that xmxg 3: + and3

42:1 kxxg , find the values ofm and k.

Answer:- k=1

6; m = 4

5. Given the inverse function2

32)(1

=

xxf , find

(a) the value off(4),(b) the value of k iff1 (2k) = k 3 .

Answer:-(a)11

2(b)

1

2

6. Given the function : 2 1f x x and : 2

3

xg x , find

(a) f1 (x) ,

(b) f 1 g(x) ,(c) h(x) such that hg(x) = 6x 3 .

Answer:-(a)1

2

x+(b)

1 1

6 2x (c) 18x + 33

7. Diagram 1 shows the function3

:2

p xg x

x

+

, 2x , wherep is a constant.

Diagram 1

Find the value ofp.

Answer:- p = 4

8.

x y z

4 4 4

2 2 2

0 0 0

1

2 2 2Diagram 2

7

3

2

p x

x

+

x

g

5

g(x) = 4 3xfg(x) = 2x + 5


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QUADRATIC EQUATIONS

1. One of the roots of the quadratic equation is twice the other root.

Find the possible values ofp.

Answer ; 5 7,p =

2. If one of the roots of the quadratic equation is two times the other root,

find an expression that relates .

Answer : 22 9b ac=

3. Find the possible value ofm , if the quadratic equation has two equal

roots.

Answer ;

4. Straight liney = mx + 1 is tangent to the curvex2 +y2 2x + 4y = 0. Find the possiblevalues ofm.

Answer : 1

2or 2

5. Given2

and

2

are roots of the equation k x(x 1) = 2mx.

If + = 6 and = 3, find the value of kand ofm.

Answer : k = 2

1, m =

16

3

6. Find the values of such that the equation (3 )x2 2( + 1)x + + 1 = 0 has equalroots. Hence, find the roots of the equation base on the values of obtained.

Answer : = 1; roots: = 1, x = 1; = 1, x = 0



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QUADRATIC FUNCTIONS

1. Diagram 1 shows the graph of the function ( )2

2 5y x p= + , where p is constant.

Find,

(a) the value of p ,(b) the equation of the axis of symmetry,

(c) the coordinate of the maximum point.

Answer:- (a) p = 2 (b) x = 2 (c) ( 2, 5 )

2.

Diagram 2 shows the graph of the function ( ) ( ) 21 2f x p x x q= + + .(a) State the value ofq .

(b) Find the range of values ofp .

Answer:-(a) q = 2 (b)1

2p

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1 Function Enrichment PDF August 14 2009