Oblast definisanosti funkcije

Oblast definisanosti funkcije Odrediti oblast definisanost finkcije: x3 1. y   x5

x 2.y   x2

x 3. y    x2  4

x6 4. y    x2  4

3x  4 5. y    2 x  6x  8

3x  1 6. y    2 x  4x  3

x2  16 7. y    x2  5x  4

x2  4x  3 8. f x    x2  6x  5

x2  2x 9. y    x2  3x  2

10. y 

 x2

11. y 

 3x  2

13. y 

 9  x2

14. y 

8  2x  x2

16. y 

 12  x  x2

17. y 

3   x2  5x  6

12. y  15. y 

4  1x

6   x2  3x  2

18. y 

5  5x

3x 19. y     3x

1 20. y   x    x

x2  3x  4 22. y   2 6xx

 1  x2 23. y   x

2x  1 24. y     x2

x 25. y     2  x  x2

x  26. y     x  1  x3

27. y  2x 

28. y 

  x  2  12  x  x2

29. y 

x

x5 21. y     4x  x2  3

4   x3  5x

  3xx2

 31. y  2 x2

32. y  2

34. y  log2 x

35. y  log 1 x

37. y  lgx  2  lgx  2

38. y  logx2  4

40. y  log2x2  x  6

41.y  log 2 4  x2  

 x2  4x

30. y  2  x2  33. y  4

5  x2  9

 2x3

36. y  log 3 x  5

2

39. y  log 4 x2  4x   36  x2

42. y  log 2 2x2  5x  3  log 1 x2  2x 3

log 2 3x2  2x  8 43. y    x5

 9  x2 44. y   log3x  5

x2 46. f x  arccos  2x

47. f x 

48. y 

3  2x  3  x  arcsin  5

x1  4  x2  arcsin  2x  1

x  49. y  arccos   1  x2 1x

50. y 

  log5x  x2 

x2  4x  3 45. y  log   x2  6x  8

domen funkcije - zadaci za vežbu.nb

2

x1 x  51. y  log   x2  4  sin  2x  7 2  5x 52. f x    2 ln x  2 rešenje: 1. x   , 5  5, 

2. x   , 2  2, 

3. x  R

4. x   , 2  2, 2  2,  5. x   , 2  2, 4  4,  6. x   , 1  1, 3  3,  7. x   , 1  1, 4  4,  8.x   , 1  1, 5  5, 

9. x   , 1  1, 2  2, 

10. x  2

2 11. x    3

12. x  1

13.x  3, 3

14. x  0, 2

15. x  (  ,1] [2, )

16. x  (  , 3 ] [ 4, ) 19. x  (  , 3 ] (3, ) 22. x  [ 4 ,  3 ) [ 1, 2) 25. x  1, 2

20. x  [ 1 ,0 ] [ 1, ) 23. x  [ 1 ,0 ) (0, 1] 26. x  3, 

28. x  2, 4

29. x  3, 5

31. x  2,  34. x  0 37. x  2,  40. x  ,

17. x  R

 32   2,

21. x  (  , 5 ] ( 1, 3) 24. x  2 27. x  0, 4 30. x  R

32. x  0, 3

33. x  [  32 , )

35. x  0

36. x  5

38. x  , 2  2,  

18. x  R

41. x  2, 2

39. x  , 0  4,  42. x   12 , 0  2, 3

43. x  ,  43   2, 5  5,  44. x   53 , 2 (2, 3 ] 45. x  , 1  2, 3  4,  46. x (  , 2][ 23 , ) 49. x   12 , 1 52. x  2, 1 ( 1, 5]

47. x  1, 3 50. x  1, 4

48. x  2,  23   0, 2 51. x  (  ,  72 ) [ 2, )