## anonymous one year ago Let f(x) = 3x2 – x + 2 and g(x) = 5x2 – 1. Find f(g(x)).

1. anonymous

@johnweldon1993

2. anonymous

Will medal AND fan <3

3. Nnesha

bec you have to substitute x for x you will get same equation so just substitute g(x) equation into f(x)

4. anonymous

I'm confused

5. Astrophysics

$f(g(x)) = 3(5x^2-1)-(5x^2-1)+2$ notice we take the function g(x) and plug it everywhere there is an x in f(x) which means f(g(x)).

6. Astrophysics

$f(g(x)) = 3(5x^2-1)^2-(5x^2-1)+2$ this is the proper one

7. anonymous

Ok. I see

8. Astrophysics

Now you may simplify it :)

9. anonymous

Can you wait until I finish so you can check my answer? :)

10. anonymous

15x^2-3-5x^2+7 yes?

11. Astrophysics

Mhm, not quite, notice it's $3(5x^2-1) \huge ^{2}$

12. anonymous

Ok. I don't understand

13. Astrophysics

$(5x^2-1)^2 \implies (5x^2-1)(5x^2-1)$

14. anonymous

Ohh! Okay

15. Astrophysics

Yup :)

16. anonymous

25x^4-10x^2+1

17. Astrophysics

Awesome, now lets multiply it by 3 $3(25x^4-10x^2+1)$

18. anonymous

75x^4-30x^2+3

19. Astrophysics

That's great :D, now we have $75x^4-30x^2+3 -(5x^2-1)+2$

20. Astrophysics

Now simplify it a bit more

21. anonymous

75x^4-30x^2-5x^2+3

22. Astrophysics

Good one more step though, look for like terms

23. anonymous

75x^4-35x^2+3

24. Astrophysics

Yup, nice work!!

25. anonymous

Is that it?

26. Astrophysics

Yup, we're done :)

27. anonymous

28. Astrophysics

$f(g(x)) = 75x^4-35x^2+3$

29. Astrophysics

Unless you want solutions to it as well, but I doubt it, since it's gross...and sure :)

30. anonymous

Lol okay thanks :)

31. Astrophysics

And we are solving for x? :)

32. anonymous

Solve the equation for the variable. Show each step of your solution process.

33. Astrophysics

Sounds fun, any idea how to start

34. anonymous

And yes :) You know, the usual

35. Astrophysics

See if you can do anything with the 4

36. anonymous

subtract it from 5?

37. Astrophysics

Yup

38. Astrophysics

|dw:1434493963942:dw| so far so good right

39. Astrophysics

Now do you know how to deal with the square root

40. anonymous

square both sides?

41. Astrophysics

Yes! And I'll show you why exactly we do that, so it makes sense...so when we have squareroot anything it means this $\huge \sqrt{x} \implies x^{1/2}$ and notice if we square it we get 2/2 hence x^1 :), so squaring both sides would be the proper thing to do!

42. anonymous

Yay :)

43. Astrophysics

Alright so we should have what now?

44. anonymous

45. Astrophysics

|dw:1434494236543:dw|

46. anonymous

So, subtract 3 I meant

47. Astrophysics

Yes :), and our answer will be? :D

48. anonymous

x=-2

49. Astrophysics

Yes!! |dw:1434494432642:dw|

50. anonymous

HAHAHA :D Yesssss

51. anonymous

Ok last one, and I'm done. Pleaseeee

52. Astrophysics

Lol ok ok

53. anonymous

Given the expression 5a2b – 13ab + 7a3 – 4b, do the following as instructed below: Write the polynomial in descending order. Classify the polynomial by the number of terms. State the degree of the polynomial.

54. anonymous

Thank you friend!! *Huge internet hug*

55. Astrophysics

Ok lets do it step by step, descending order just means greatest to least (look at the a's). So go ahead and do that now :)

56. anonymous

Isn't it greatest to least?

57. Astrophysics

Yes, I made a mistake xD

58. Astrophysics

Tried to fix it before you saw haha, but nice catch!

59. Astrophysics

Good! Now lets state the terms, and figure out what kind it is!

60. anonymous

polynomial?

61. Astrophysics

Yes, but I think they might want you to say quadrinomial (meaning 4)

62. anonymous

oh okay :)

63. anonymous

64. Astrophysics

degree is the highest number of the variables, so we have to sum up the variables for the highest degree, can you figure out which one? :)

65. anonymous

3

66. Astrophysics

Yup, and that's it!

67. anonymous

:( Thank you so much for all your help! You were probably the nicest tutor on here I've met so far!!!

68. Astrophysics

Haha, thanks and your welcome :)