## anonymous one year ago Let f(x) = -2x - 7 and g(x) = -4x + 3. Find (f o g)(-5)

1. jim_thompson5910

(f o g)(-5) is the same as f(g(-5)) the first task is to find g(-5). Do you know how to do this?

2. anonymous

A. -53 C.23 D.3

3. anonymous

No i have no clue

4. anonymous

@satellite73

5. anonymous

Could you help @jim_thompson5910

6. anonymous

@SolomonZelman

7. jim_thompson5910

g(x) = -4x + 3 g(-5) = -4(-5) + 3 ... replace every x with -5 g(-5) = ??

8. misssunshinexxoxo

On OS we help people learn; Jim is trying to make sure you are understanding this

9. anonymous

Oh i know and i defiantly want the help

10. UsukiDoll

(f o g)(-5) well first let's do (f o g ) which means that the g(x) equation is placed inside the f(x) equation

11. anonymous

20+3

12. UsukiDoll

whoa... let's do this step by step

13. anonymous

Oh sorry i was replying to what @jim_thompson5910 started

14. jim_thompson5910

so you should find that g(-5) = 23 agreed?

15. anonymous

correct

16. jim_thompson5910

f(g(-5)) becomes f(23) after you replace g(-5) with 23

17. jim_thompson5910

now follow the same basic steps to calculate f(23)

18. UsukiDoll

ok it's ok didn't see that :) anyway given the functions f(x) = -2x-7 and g(x) = -4x+3 we need to place g(x) =-4x+3 into the f(x) so for every x in f(x) the g(x) takes it's place

19. UsukiDoll

so the end result should be -2(insert g(x) function here)-7

20. UsukiDoll

then combine like terms and evaluate when x = -5

21. anonymous

im lost

22. anonymous

23. jim_thompson5910

no

24. UsukiDoll

I agree with jim there's more to be done...

25. anonymous

ok im ready to learn the rest

26. UsukiDoll

27. anonymous

No i got lost after we got f(23)

28. jim_thompson5910

To calculate f(23), replace every x in f(x) with 23 f(x) = -2x - 7 f(23) = -2*23 - 7 f(23) = ??

29. UsukiDoll

that means x = 23 evaluate the f(x) function

30. jim_thompson5910

it's just like the g(x) one

31. anonymous

-46

32. anonymous

f(23)=-46-7

33. jim_thompson5910

keep going

34. UsukiDoll

almost there

35. anonymous

46-7=39

36. UsukiDoll

we have two negative numbers so the negative numbers are supposed to increase, not decrease

37. anonymous

opps wrong

38. anonymous

-53

39. UsukiDoll

yes!

40. jim_thompson5910

good

41. UsukiDoll

do you want to see another method of solving this equation as a reference?

42. anonymous

yay we did it

43. anonymous

yes that would be great

44. UsukiDoll

ok so here's how I would tackle this problem (f o g ) (-5) first I will tackle f o g portion and then evaluate when x = -5 so f o g means that we place our g(x) function inside all x's of the f(x) function f(x) = -2x-7 and g(x) = -4x+3 f o g -2(-4x+3)-7 distribute the -2 8x-6-7 8x-13 so our f o g = 8x-13 now evaluating when x = -5 f o g (-5) = 8(-5)-13 = -40-13 = -53

45. anonymous

Can you guys help me solve another @UsukiDoll @jim_thompson5910

46. UsukiDoll

sure

47. anonymous

Let f(x) = x + 2 and g(x) = x2 Find ( g o f)(-5)

48. UsukiDoll

$\large f(x) = x+2, g(x) = x^2$

49. UsukiDoll

this is similar to the previous problem. while our x still remains the same g o f means that we place our entire f(x) function inside the x's of the g(x) function so g o f = (insert f(x) here)^2

50. anonymous

so is x -2?

51. UsukiDoll

our f(x) = x+2 and we need place it inside g(x). Since g(x) =x^2 g o f = (f(x) function)^2

52. anonymous

so X^2+X+2?

53. UsukiDoll

$g o f =(x+2)^2$ that second power means write (x+2) two times after that, we need to use FOIL to expand

54. anonymous

your gonna have to hold my hand on this one cuz im totally lost lol im sorry

55. UsukiDoll

alirght.. so we write (x+2) two times (x+2)^2 means (x+2)(x+2) now using FOIL (x)(x)+2(x)+2(x)+(2)(2) so what's 2 x 2 2x + 2x and x times x I guess that's the closest way of notating multiplication

56. anonymous

Ok so where do we go from this?

57. UsukiDoll

first tell me what 2 x 2 is then tell me what 2x+2x is .. I will factor out the x to make it easier x(2+2)

58. anonymous

2x2=4

59. anonymous

2x+2x=4X

60. UsukiDoll

mhm last one what is (x)(x) . I'll make this easier by rewriting it and using the addition exponential rule, $\large (x)(x) \rightarrow x^1x^1 \rightarrow x^{1+1}$ so you just have to solve for the exponent part. what is 1+ 1

61. anonymous

2

62. anonymous

$x ^{2}$

63. UsukiDoll

yes so now we have $g o f =x^2+4x+4$

64. UsukiDoll

so now we evaluate this when x = -5. so replace all x's with -5

65. anonymous

25-20+4=9

66. UsukiDoll

$g o f (-5) =(-5)^2+4(-5)+4$ $g o f (-5) =25-20+4 \rightarrow 5+4 = 9$ correct

67. anonymous

Thank you very much