## anonymous one year ago i need some help

1. anonymous

2. IrishBoy123

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3. IrishBoy123

have you got your equation for $$f^{-1}(x)$$ yet??

4. anonymous

idk how to do anything with it my teacher never taught me how

5. IrishBoy123

first, we'll re-write your equation as y = 2x - 6, so this takes in x values and returns y values now switch that around so that it says x = ... ie give me an equation that takes in y values and returns x values [you'll see what the point of this is when we're done]

6. anonymous

so takes in is the 2x-6 part and puts out is y=

7. IrishBoy123

yes now switch it around so it says x = ....

8. IrishBoy123

example y = 2x +1 x = y/2 - 1/2

9. IrishBoy123

example y = 9x - 3 x = (1/9) (y+3)

10. anonymous

y-1/2=x

11. IrishBoy123

example i start with y = 2x +1 i switch around to get x = y/2 - 1/2 example i start with y = 9x - 3 i switch around to get x = (1/9) (y+3) you are starting with y = 2x - 6 can you switch it around in same way?

12. IrishBoy123

you can do it!

13. IrishBoy123

i can do the first example is steps, if that helps??!!

14. anonymous

x=y/2-2/1

15. IrishBoy123

??

16. anonymous

idk im lost

17. anonymous

thats what i thought

18. IrishBoy123

x=y/2-2/1 for you question?!?!?

19. anonymous

yes

20. IrishBoy123

i'll try this 1st example $$y = 2x +1$$ add -1 to each side $$y-1 = 2x +1-1$$ so $$y-1 = 2x$$ divide each side by 2 $$y/2-1/2 = 2x/2$$ so $$y/2-1/2 = x$$ just switch left hand and right hand sides around $$x = y/2-1/2$$ and that is done

21. anonymous

and thats what u want me to find for my prob

22. IrishBoy123

2nd example $$y = 9x - 3$$ add 3 to each side $$y +3= 9x - 3+3$$ so $$y +3= 9x$$ divide each side by 9 $$(1/9)(y +3)= 9x/9$$ so $$(1/9)(y +3)= x$$ switch around $$x=(1/9)(y +3)$$

23. IrishBoy123

yes if you truly have not been shown how to do this algebra, then you should really not be trying to do inverse functions...

24. anonymous

i must have missed that class but yeah

25. IrishBoy123

well copy what i did and see how you go.

26. anonymous

x=(y/2)+(2/6)

27. IrishBoy123

very good we can simplify a little, ie the 2/6, right?

28. anonymous

yes 3

29. anonymous

what happens now

30. IrishBoy123

i'll do this bit as it's just notation, important notation but you havealready done the hard bit you recall we took your function $$f(x) = 2x - 6$$ and re-wrote as $$y = 2x - 6$$ so we could manipulate it a bit easier well we now take your solution for the inverse ie $$x=y/2+3$$ and we re-write it as $$f^{-1}(x) =x/2 + 3$$ so or example $$f(3) = 0$$, and hey presto $$f^{-1}(0) = 3$$!!! so you now take $$f^{-1}(x) =x/2 + 3$$ and answer the question

31. IrishBoy123

they want $$f^{-1}(2)$$

32. anonymous

alright i followed and understood upto f(3)=0 and then i got lost

33. IrishBoy123

no worries function $$f(x) = 2x - 6 = 0 \implies f(3) = 2(3) - 6 = 0$$ inverse function $$f^{-1}(x) = x/2 + 3 \implies f^{-1}(0) = 0/2 + 3 = 3$$!! so we have function f and its inverse $$f^{-1}$$. they reverse each other plugging into $$f^{-1}(x) = x/2 + 3$$ for x = 2 $$f^{-1}(2) = (2)/2 + 3$$

34. anonymous

okay i think i get it

35. anonymous

so doo i solve f−1(2)=(2)/2+3

36. IrishBoy123

yes

37. anonymous

f=1/2

38. anonymous

no thats wrong

39. IrishBoy123

yes, go again

40. anonymous

5

41. anonymous

-5

42. IrishBoy123

$f^{-1}(2) = \frac{(2)}{2} + 3$

43. anonymous

im lost a little

44. anonymous

what do i do with f^-1(2)

45. anonymous

so i just solve the answer part

46. IrishBoy123

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47. IrishBoy123

yes just solve

48. anonymous

f−1(2)=4

49. IrishBoy123

indeed

50. anonymous

51. IrishBoy123

yes

52. anonymous

okay