## anonymous one year ago Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)?

1. UsukiDoll

given: g(x) = 3x-9 f(x) = 5x-1 and we need to solve g(x) - f(x)

2. UsukiDoll

so we plug these functions into g(x)-f(x) 3x-9-(5x-1) now distribute the negative on the right hand side of the equation

3. anonymous

3x-9(-5x+1)?

4. UsukiDoll

ok... that's good 3x-9-5x+1 now we combine like terms.. we can also rearrange this equation to make it easier to solve so instead of 3x-9-5x+1 we can rewrite it as 3x-5x-9+1

5. anonymous

oh the equation is 3^x

6. anonymous

im sorry

7. UsukiDoll

ahhhhhhhh! ok no problem... just rewrite what f(x) and g(x) was supposed to be

8. UsukiDoll

ok was g(x) = 3^x-9 ?

9. anonymous

f(x)=5x-1 g(x)=3^x-9

10. anonymous

@jim_thompson5910

11. UsukiDoll

ok we do the same process again g(x) -f(x) 3^x-9-(5x-1)

12. UsukiDoll

actually we have already done the distribution of the negative, 3^x-9-5x+1 now combine like terms for -9+1

13. anonymous

-8

14. UsukiDoll

$3^x-9+1-5x$

15. UsukiDoll

yup $3^x-8-5x$

16. UsukiDoll

since we can't combine any more terms, that's the answer

17. anonymous

Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) • g(x)? f(x) • g(x) = log10 x5x − 2 f(x) • g(x) = log10 (5x − 2)x f(x) • g(x) = 5x log10 x + 2 log10 x f(x) • g(x) = 2 log10 x − 5x log10 x

18. anonymous

let me type the equation correctly

19. anonymous

$f(x)=\log_{10} x$ g(x)=5x-2

20. anonymous

firt answer is log10 x^5-2 second is log10(5x-2)^x

21. anonymous

@jim_thompson5910

22. UsukiDoll

we are using multiplication $f(x) \cdot g(x)$ once again we place our f(x) function and g(x) into the formula

23. UsukiDoll

$\log10_x[5x-2]$ use distribution

24. anonymous

what do you distribute

25. UsukiDoll

distribute the log

26. UsukiDoll

$\log_{10}x[5x-2]$

27. anonymous

i dont have a graphing or scientific calc to solve

28. UsukiDoll

we can just distribute the log |dw:1435728843362:dw|

29. anonymous

x(log10 5x-log10 2)?

30. UsukiDoll

|dw:1435728950642:dw| now distribute the log with the negative -2

31. UsukiDoll

distribution is multiplication what's that log times -2?

32. anonymous

idk i dont have a calc

33. UsukiDoll

we don't need a calculator this time

34. UsukiDoll

$\log_{10}x[5x-2] \rightarrow \log_{10}x[5x]-\log_{10}x[2]$ based on your choices, it doesn't require you to calculate the log portion

35. anonymous

so its either c or d?

36. anonymous

wouldnt it be d because its - and not +?

37. UsukiDoll

I'm not sure.. @jim_thompson5910 can help out.. I need to go

38. anonymous

@jim_thompson5910

39. jim_thompson5910

This question right? Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) • g(x)? f(x) • g(x) = log10 x5x − 2 f(x) • g(x) = log10 (5x − 2)x f(x) • g(x) = 5x log10 x + 2 log10 x f(x) • g(x) = 2 log10 x − 5x log10 x

40. anonymous

yes and i corrected how it is right under neath that

41. jim_thompson5910

$\Large f(x) = \log_{10}(x)$ $\Large g(x) = 5x-2$ You will distribute the "log(x)" portion through like so $\Large f(x) \cdot g(x) = \log_{10}(x)\cdot(5x-2)$ $\Large f(x) \cdot g(x) = \log_{10}(x)\cdot 5x + \log_{10}(x)\cdot(-2)$ $\Large f(x) \cdot g(x) = 5x\log_{10}(x)-2\log_{10}(x)$

42. anonymous

so d?

43. anonymous

its backwards but

44. jim_thompson5910

can you post a screenshot of the full thing? some symbols didn't make it (at least I think?)

45. anonymous

46. jim_thompson5910

D is close but not quite 100%

47. jim_thompson5910

there has to be a typo that they made

48. anonymous

49. anonymous

could it be c because when you multiply its equivalent to adding with exponets or something like that lol?

50. jim_thompson5910

hints: * look at rule 2 at the link below http://www.purplemath.com/modules/logrules.htm * factor 5x-5 and you'll see something cancel

51. anonymous

52. jim_thompson5910

$\Large f(x) = \log_{3}(5x-5)$ $\Large g(x) = \log_{3}(x-1)$ Use rule 2 from that link $\Large f(x)-g(x) = \log_{3}(5x-5)-\log_{3}(x-1)$ $\Large f(x)-g(x) = \log_{3}\left(\frac{5x-5}{x-1}\right)$ $\Large f(x)-g(x) = \log_{3}\left(\frac{5(x-1)}{x-1}\right)$ $\Large f(x)-g(x) = \log_{3}\left(\frac{5\cancel{(x-1)}}{\cancel{x-1}}\right)$ $\Large f(x)-g(x) = \log_{3}\left(5\right)$

53. anonymous

i thought we were on the other one still lol but yeah it make since now that i know what were talking about

54. jim_thompson5910

oh the other one has a typo I think

55. anonymous

which would you pick

56. jim_thompson5910

D I guess since it's close just off by a sign

57. anonymous

it was wrong i guess it was c

58. anonymous

thanks thoough!

59. jim_thompson5910