## anonymous one year ago Given the functions f(x) = 3x + 2 −4/x and g(x) = 2 − 3x, find the indicated values. a) f(a + b) b) g(a) − g(a − b) + f(a)

1. anonymous

replace x in the equation above with (a+b)

2. anonymous

f(a+b)=3(a+b)+2 -4/(a+b)

3. xapproachesinfinity

wherever you x replace by a+b $f(x)=3x+2-\frac{4}{x}$ $f(\color {red}{a+b})=3(\color{red}{a+b})+2-\frac{4}{\color{red}{a+b}}$

4. xapproachesinfinity

if for example f(x)=x^-2 they ask f(c) $f(\color{blue}{c})=\color{blue}{c}^2-2$ just a matter of replacing the dummy variable

5. anonymous

whats a+b tho

6. anonymous

what do i do when i set it up like that

7. xapproachesinfinity

that's what they asked you the evaluate a+b standards as some variable

8. xapproachesinfinity

hmm you can simply more if they ask you just depends on the question

9. xapproachesinfinity

in this case i would just leave it that way

10. anonymous

11. xapproachesinfinity

second you gonna do each one separately g(a) g(a-b) f(a) after that the results do g(a)-g(a-b)+f(a)

12. xapproachesinfinity

let me see if you can do g(a)

13. anonymous

i thought were supposed to use the equation they gave us tho

14. anonymous

i dont know

15. xapproachesinfinity

what equation?

16. anonymous

the second part

17. xapproachesinfinity

you have g(x) right find g(a) by replacing x with a

18. xapproachesinfinity

i broke it down to steps as you can see first find g(a) then g(a-b) then f(a) all separately

19. xapproachesinfinity

try to do g(a) first let me see you do it

20. anonymous

so 2-3(a)?

21. xapproachesinfinity

yes g(a)=2-3a what about g(a-b) now

22. xapproachesinfinity

use the same function g(x)=2-3x to find that

23. anonymous

2-3(a-b)?

24. xapproachesinfinity

yes good

25. xapproachesinfinity

now f(a)

26. anonymous

2-3(a)-2-3(a-b)+3(a)+2-4/(a)?

27. xapproachesinfinity

that the next step let's not skip do f(a) first

28. xapproachesinfinity

i mean you have the idea but that's wrong because of the sign

29. anonymous

3(a)+2-4/(a)

30. xapproachesinfinity

yes now g(a)-g(a-b)-f(a)=2-3a-(2-3(a-b))+3a+2-4/a

31. xapproachesinfinity

the difference btw what i just did and what you did is i put those parenthesise before 2-3(a-b) because of the sign that came before it

32. xapproachesinfinity

if ignored that it would be wrong because the sign has to be distribute to 2-3(a-b)

33. xapproachesinfinity

so no what we do it open up the parenthesis 2-3a-2+3(a-b)+3a+2-4/a

34. xapproachesinfinity

we simplify more =2-3a-2+3a-3b+3a+2-4/a =....?

35. xapproachesinfinity

finish it up

36. anonymous

oh okay, thanks so much!!

37. xapproachesinfinity

welcome!

38. anonymous

so is the final answer 3a-3b+2-4/a

39. xapproachesinfinity

yeah seems good!