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anonymous one year ago Hi I'm new to open study, If someone could please help me with these 3 questions. I cant seem to get them right. 1) Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) : f(x) = 3x2 + 2 g(x) = x − 8 2) Given the following functions f(x) and g(x), solve f[g(10)] f(x) = 10x + 8 g(x) = x + 9 3) Given the following functions f(x) and g(x), solve (f + g)(3) f(x) = 2x + 21 g(x) = x − 24

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1. phi

(f ⋅ g)(2) is short for f(2) * g(2) can you find f(2) ?

2. anonymous

I have no idea how to start.

3. phi

they give you a formula f(x) = 3x^2 + 2 f(x) is the "short name" and 3x^2 + 2 is the formula f(2) means: find the formula, find the "x" in the formula and replace the x with a 2 can you do that?

4. anonymous

So 3(2)^2+2?

5. anonymous

38?

6. phi

yes. now simplify that

7. anonymous

Is it 38?

8. phi

no. how did you get that? remember order of operations first do exponents, so first do 2^2

9. phi

2^2 means 2*2

10. anonymous

Well I replaced the x with 2. And the formula is 3x^2 + 2. Is it 16?

11. anonymous

3 times 4 is 12 and 12 plus 2 is 14. Sorry 14?

12. phi

it is worth knowing how to do this. 3*2^2 +2 first do 2^2 which is 2*2 . you get 4 so you have 3*4 +2 12+2 14 yes 14

13. phi

(f ⋅ g)(2) is short for f(2) * g(2) so far we have f(2) is 14 now we need g(2) can you do that ?

14. anonymous

Where do I start?

15. phi

to find g(2) find the formula for g replace any x's in the formula with 2 simplify

16. anonymous

How do I find the formula for g?

17. anonymous

Oh they gave me the formula

18. anonymous

g(x) = x − 8

19. phi

they give it to you. g(x) is the "name" they give to x-8 that is what g(x) = x − 8 means

20. anonymous

So g(2)=2-8

21. phi

yes, and that simplifies to what?

22. anonymous

g(2)=-6

23. phi

ok now we have (f ⋅ g)(2) is short for f(2) * g(2) so far we have f(2) is 14 and g(2) is -6 now we multiply to get the final answer

24. anonymous

14*-6=-84

25. phi

yes.

26. anonymous

Thankyou! Can you help with the other 2?

27. phi

Let's skip to Q3 (f + g)(3) f(x) = 2x + 21 g(x) = x − 24 can you guess what (f+g)(3) is short for ? (based on the first question)

28. anonymous

f(3) and g(3)

29. phi

it would be better to say f(3) + g(3)

30. anonymous

f(3)=2(3)+21 f(3)=27?

31. phi

yes

32. anonymous

So g(x) = x − 24 g(3)=3-24 g(3)= -21?

33. phi

yes

34. anonymous

And 27*-21 is -567

35. phi

ok, but we are doing (f + g)(3) = f(3) + g(3)

36. anonymous

Ok so what do we do know that we know what f and g are?

37. phi

the + means add

38. anonymous

27+(-21)=6

39. phi

yes. notice in Q1 we have multiply (that is what the dot means) and in this question we are adding we might also see (f-g)(3) (subtract) or (f/g)(3) divide

40. phi

now Q2 this one is a bit different. The formulas are not combined using add or multiply we have something called "composition" (they have to call it something)

41. anonymous

Im still stuck on 3

42. anonymous

My answer choices are: 98 198 190 2052

43. phi

those are the choices for (f + g)(3) where f(x) = 2x + 21 g(x) = x − 24 ??

44. anonymous

Yes

45. phi

those look like the choices for Q2 which we have not done yet

46. anonymous

Oh Im sorry I got confused

47. anonymous

The answer was 6 sorry

48. anonymous

Ok we can do #3 now

49. phi

Q2 solve f[g(10)] f(x) = 10x + 8 g(x) = x + 9 think of g(10) as some number (which it is) let's find g(10) can you do that ?

50. anonymous

Ok so g(10)=10+9?

51. phi

yes, and that simplifies to 19 so g(10) is 19 if we replace g(10) with 19 in f[g(10)] we get f(19) (the [ vs ( is just to make it easier to read in f[g(10)] ... but it means the same as parens) anyway we have figured out that f[g(10)] is the same as f(19) now we need to find f(19)

52. anonymous

f(x) = 10x + 8 So f(19)=10(19)+8?

53. phi

ok, and what number do you get?

54. phi

you do 10 times 19 then add 8

55. anonymous

198?

56. anonymous

Thankyou so so much. I got a 100%! I havent gotten a 100% before. You're a really good tutor!

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