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Chapter 1: Functions Name:EXERCISE

Inverse Functions

1. Given the function 35: xxf , find 1f .

2. Given the function2

3,

32

3:

xx

xg , find1g .

3. Given the function 3,3

12)(

xx

xxf , find

1f .

4. Given the function xxf 25)( , find(a) )4(1f ,(b) )4(1ff .

5. Given that 1,12)(1

xx

xg , find 1g .

6. Given that 2)( xxf and 32)( xxg , find 11 fg .

7. It is given that qxqx

pxxg

,)( , and 1,1

12)(

1

xx

xxg .

8. Given the function 23)( xxf and 4,4

2)(

xx

xxg , find

(a)

)(

1

xgf

,(b) )3(1fg .

Composite Functions

9. Given the functions 13: xxf and xxg 21: , find the value of )1(fg and of )1(gf .10. Given the function

12

1: xxf

and 23:

xxg .Find

(a) the value of )2(gf ,(b) the value ofx such that xgf 2)2( .

11. Given the function 25)( xxf and 43)( xxg , find the composite functionfg.

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12. Given the functions xxhxxgxxf 21)(and15)(,4)( . Find(a) .and,,,,, hhffhfghfhgffg ,(b) the value of )1(and)1( hggf ,(c) the value ofx such that xhggf 10)1()1( .

13. Given the function34: xxf

and 24: xxg .

Find

(a) )(xfg and )(xgf .(b) the value ofx such that 3)( xfg ,(c) the value ofx such that 6)( xgf ,(d) the value ofx such that )(xfg = )(xgf .

14. It is given that 23: xxf and 1,1

2:

xx

xxg .

Find the value ofx such that gffg .

15. Given the functions baxxh )( , where a and b are constants, a > 0 and 2536)(2 xxh .Find the value ofa and b. [SPM 2007, P1, 3M]

16. Given the function 34: xxf and its composite function 12: xxfg , find g(x).17. Given the function 23: xxg and 1: xxgh , find )(xh .18. Given the function 12)( xxf and 43)( xxgf , find g(x).

19.

The functionfis defined by 3:

xxf . Another function g is such that 76:

2

xxxgf .Find the function g.

20. Function fand g are defined by 23)( xxf and baxxg )( . Given that 49)( xxfg , find(a) the value ofa and ofb,(b) the values ofx such that 18)( 2 xxfg .