## lavalava 3 years ago use the function to answer the question: x+14 if x<-7 f(x) 21 if -7 ≤x<-6 x^2 -1 if x ≥ -6 what is the value of f(-6)?

Since u want to find F(x) at x=-6 , U will use the Function F(x)= x^2-1 because x is bigger or **Equal** -6 Plug -6 in the equation so it will be F(-6)=(-6)^2-1=.....

2. lavalava

35?

3. hartnn

yup,35

Bingo!

5. lavalava

what about f(x)=x^2-4; g(x)=x+2 which is equal to (f+g)(x)

U mean Find F(F(x)+g(x)) ?

7. lavalava

no its f(x)+g(x) im not to sure but i think that might be it

8. hartnn

then just add them x^2-4+x+2 = ?

9. lavalava

x^2+x-2?

10. hartnn

yup

11. lavalava

okay so what is f(x)=4x-1 g(x)=5x^2 which is equal to (fºg)(x)?

12. hartnn

for (fog)(x) , replace 'x' in f(x) by g(x) = 5x^2

13. lavalava

so then : 4(5x^2)-1

14. hartnn

yup, that will be 20x^2-1

15. lavalava

and then what is f(x)=4x-7 g(x)=x+3 what is the function of (gºf)(4)

16. lavalava

is it 12?

17. hartnn

to get (gof)(x) replace 'x' in g(x) by f(x) and then put x=4

18. hartnn

yup, its 12

19. lavalava

what is f(x)=5x-10 what is the value of f^-1 (-3)

20. hartnn
21. hartnn

so got that, its 1.4

22. lavalava

yea

23. hartnn

any more questions to come ?

24. lavalava

yea

25. lavalava

what is the vertex of the graph of f(x)=-2|x-5|+3

26. lavalava

i think its -5, 3

+5,3

28. hartnn

nopes, (5,3) vertex for f(x) = p|x+a|+b is -a,b

29. lavalava

ohhh okay

30. lavalava

the graph of g(x) results when the graph of f(x)=-|x| is shifted 3 units to the left. i think it's g(x)=-|x+3|

31. lavalava

what is the value of f(-4) when f(x)= -10 if x< -5 x^3 if -5≤x≤2 2x+4 if x>2

32. hartnn

in which range does -4 lie ?

33. lavalava

the middle one and the last one

34. hartnn

not the last one, x>2 means x cannot be -4 so only middle one. put x= -4 in middle function, what do u get ?

35. lavalava

-64

36. hartnn

37. lavalava

okay now this one is kinda confusing to me but i think i know the answer....

38. lavalava

i think it is the third one, but im not too sure....

39. hartnn

nopes, its 4th. put these values, x=0,0.5,1,1.5,..., find g(x) u will get it

40. lavalava

ohhhh i get it!!! its soo confusing sometimes!

41. lavalava

f(x)=2x+5 g(x)=3x^2 which is equal to (fºg)(x)? i tried it and i got 3x^2+2x+5 but i think it's wrong....

42. hartnn

put x= 3x^2 in f(x) 2(3x^2)+5 = ?

43. lavalava

6x^2+5?

44. hartnn

yup.

45. lavalava

omg you make it easier to understand hahaha

46. hartnn

more questions ? i need to go...

47. lavalava

yea one last one f(x)=2/x g(x)=|x|-1 what is the domain of (fºg)(x)

48. hartnn

fog (x) = ?

49. lavalava

x|x=real numbers x|x ≠0 x|x≠0, x≠1 x|x≠-1, x≠1

50. hartnn

f(g(x)) = 2/(|x|-1) ok? for which values is denominator = 0 ??

51. lavalava

no the ones i put up last were the options

52. hartnn

i know. denominator should not be 0 |x|-1 should not be 0 for x=1, |1|-1=1-1=0 for x=-1, |-1|-1=1-1=0 so x|x≠-1, x≠1 got it ?

53. lavalava

ohh okay yea! thank you! you make it easier to understand ty very much

54. hartnn

welcome :)