anonymous one year ago Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) and select the correct answer below: f(x) = 3x2 + 2 g(x) = x − 8 −42 −84 42 84

1. anonymous

@iGreen

2. misty1212

HI!!

3. anonymous

hi :D

4. misty1212

$f(x)=3x^2+2$ right?

5. anonymous

Yeah

6. misty1212

ok then ' $f(2)=3\times 2^2+2$ what is that number?

7. anonymous

I got 68

8. misty1212

think you did the "order 'o operations" wrong square first, then multiply

9. anonymous

How do I square?

10. iGreen

$$\sf 2^2 \rightarrow 2 \times 2$$

11. misty1212

how do you square a number? multiply it by itself so $2^2=2\times 2$

12. anonymous

so it'd be f(2)=3×2x2+2?

13. misty1212

yes what is $3\times 2\times 2+2$?

14. anonymous

14

15. misty1212

right now hold on to that number

16. anonymous

Alright

17. misty1212

$g(x)=x-8$ what is $g(2)$?

18. anonymous

g(2) = x - 8?

19. misty1212

hmmm i see you are a bit confused as to how to evaluate a function

20. anonymous

Very :/

21. misty1212

$g(x)=x-8\\ g(\spadesuit)=\spadesuit-8\\ g(\xi)=\xi -8$

22. misty1212

so how do you find $$g(2)$$? where you see an $$x$$ replace it by a $$2$$

23. anonymous

g(2) = 2 - 8? The other two functions have clovers and & signs in them, not sure if it's meant to be there.

24. misty1212

yeah$g(2)=2-8$

25. anonymous

So what's the next step?

26. misty1212

find $2-8$

27. anonymous

-6, if i'm solving from left to right

28. anonymous

g(2) = -6?

29. misty1212

yes it is $$-6$$ no matter what you do

30. misty1212

final step $f\times g(2)=f(2)\times g(2)=14\times (-6)$

31. anonymous

so the final answer woulds be -84?

32. misty1212

yes

33. anonymous

Thanks :)) Could you help me with a few more?

34. misty1212

lol sure we can at least do one more

35. anonymous

Sweet :)

36. anonymous

Gaming systems are on sale for 20% off the original price (g), which can be expressed with the function p(g) = 0.8g. Local taxes are an additional 12% of the discounted price (p), which can be expressed with the function c(p) = 1.12p. Using this information, which of the following represents the final price of a gaming system with the discount and taxes applied? c(p) + p(g) = 1.92g c[p(g)] = 0.896g g[c(p)] = 1.92p c(p) ⋅ p(g) = 0.896pg

37. anonymous

This seems like an easy one, it's just the trouble of setting up the function I guess

38. misty1212

it is easy it is the last one

39. anonymous

How did you get that?

40. misty1212

lets do it with an item that cost $100 41. misty1212 first take the 20% discount, multiply $100\times .8=80$ 42. misty1212 so it is$80 before the tax then put in the tax get $80\times 1.12=89.6$

43. misty1212

what did we do? first multiply by $$.8$$ then multiply by $$1.12$$

44. misty1212

ohh hold the phone for a second

45. misty1212

i see what they want you to say, they want you to pick B

46. anonymous

Oooh so it's B?

47. misty1212

first do $$p$$ then do $$c$$ it is $c(p(g))$

48. misty1212

which is kind of silly since you can do it just by multiplying, but whatever pick B

49. anonymous

Alright that's what I was thinking too haha, thank you. Couple more :D?

50. anonymous

Or would you rather me open a new question to give you another best response?