1

1. x x x xf x 36 225 3 4 3 25 .

f 0 5 f 0 3 f 0 40 f 0 1052log log log log 0

f 0 2 f 0 11 f 0 77 f 0 32

2. x x x x3 4 2 5 4 3 5 2

x xf x 3 4 2 5 x x

g x 4 3 5 2

f

3. f x log log x 1 .

f.

f

f x 7 f x 1 log2 .

3f 101 2f 1001 f 10001 log18

4. xf x ln e 1 1 x

g x ln 2e 2 .

f,g.

f,g

f 2x g x 1 .

g 1 x f x ln2

5. 2f x log x 1 log x 2x g x 1 log x 1 .

f,g.

i. f x 0 ii. g x 0 .

f 4 3g 1 4 log30 .

6. 2f x log 2x 4x 4 2logx .

f

2x 1 f 1 xf 1 f 1

10 5 10 10 f 2

f 1 logxx 2

2f 1 logxx 2 2

7.

x 1f x ln x

1 x

f.

f

2

1 1f , f , f 0

2 2.

f x f x 1 1 2x 0 .

8. 4 2

f x logx 8 logx log 100x ,x 0 ,

f

M 10,25 .

i. f 2

2f x log x 4logx

ii. f x 0 .

9.

2x

x

e 1f x ln

e 5.

)

) f x 2ln2 .

) f x 0 .

f xxg x e 5 e .

i. g -1.

ii. g x x g x

10. 2x xf x ln e 2e 3 x

g x ln3 ln e 1 .

) f g.

) f x g x

) f x 2g x .

g 1 1.

g x g 1 f 0

11.

2x x

1 1f x 2 3 1

5 5

xg x 5 .

50125 5 1

g x g x 1 g x 2 ..... g x 494

12. 2x xf x ln e 4e 3

x x .

.

3

13. 2x x

x

f x x

f x x 2ln2

f -

2x 1 x2x 1 e x e

14. 2x xf x ln e 6e 8 .

.

f x ln3

f x x ln3

15. x

3f x 5 .

x 1 x 3 x 4 x 2f 7 3 5 f 3 5 .

f

A 1,19 .

3 f x f x 2

16. x x1f x e e

2 x x1

g x e e2

.

f g

2 2f x g x 1 x .

g g f g f , , .

f x 2g x 1.

17. 2f x logx .

f

g x f x 2

y 2log4 .

18. f x log x 4 3 .

f

k k, 2 f.

x 3 x x x 3f 3 2 f 23 3 2

4

19.

log 3x 14f x

log x 4.

f y 2 .

f y 1.

20. f x ln x 2 .

f

f

) 2ln x 2 f x 2 0 .

21. f x log log x 4 .

f

f x 0 .

22. x

2f x 4 4

f

1,9 .

2,3 2f x f 5x 6 .

4 x x2f x 3 9 5 6 0 .

23.

lnx 1f x

lnx 1.

f

1f x

1f

x

1 1x 0, ,e e,

e e.

1f x 1

1f

x

24.

x

4f x

2

6 7f f

7 6.

.

0 .

i. f x 1 f x 2 f x 3 48

ii. log2

2f logx log f x

iii. logx log22 x 16

5