anonymous one year ago Find the inverse of the function. f(x)=3squareroot x/8-4 i keep getting f−1(x)=512x3+6144x2+24576x+32768

1. anonymous

when these are the answer choices f-1(x) = [8(x + 4)]3 f-1(x) = 8(x + 4)3 f-1(x) = 8(x3 + 4) f-1(x) = 24(x + 4)

2. anonymous

Can you draw the function?

3. anonymous

Because it's not very clear. :)

4. Jack1

hi... is this your function? $$\Large f(x)=3 \times \sqrt{ \frac x{8-4}}$$

5. anonymous

no

6. Jack1

is it this? $$\Large f(x)=3 \times \sqrt{ \frac x8-4}$$

7. anonymous

$f(x)=\sqrt[3]{x/8}-4$

8. anonymous

Step 1: Change f(x) to y. Step 2: Flip x and y. So y will become x, and x will become y. Step 3: Make the function look like this--> y=mx+b

9. anonymous

|dw:1439341791162:dw|

10. anonymous

|dw:1439341863512:dw|

11. anonymous

Did you understand it or not?

12. anonymous

After that, make the function look like y=mx+b.

13. anonymous

so its c?

14. anonymous

No.

15. anonymous

how

16. anonymous

Add 4 on both sides. What will you get?|dw:1439342093820:dw|

17. anonymous

i was almost positive it was either c or d but now i am very confused

18. anonymous

lol

19. anonymous

then can you show me how you did it?

20. anonymous

what is funny?

21. anonymous

lol because i'm trying to hep you but it seems like you're saying that my answer is already wrong :D

22. anonymous

I am not saying that at all I am saying you are right, and i guess i started wrong form the beginning

23. anonymous

just a quick question: do you know how to add 4 on both sides?

24. anonymous

nope

25. anonymous

oh if you don't know, then you can say so. you shouldn't keep people waiting :)

26. anonymous

sorry

27. anonymous

do you remember this in algebra 1? |dw:1439342702568:dw|

28. anonymous

just a quick yes or no is fine

29. anonymous

no

30. anonymous

Wait we are both in FLVS Pre-Calculus class right? So basically, you just need to add 4 to x, and the 4 in the right side is now removed. |dw:1439342854963:dw|

31. anonymous

And then to remove the cube root, you just simply cube it. So from the left side, x+4 will now become $$\huge (x+4)^3$$. And the right side will become $$\huge\frac{ y }{ 8 }$$.

32. anonymous

ohhhhh i see

33. anonymous

The function will now look like this. Now to remove the 1/8 in y/8, simply multiply it by its reciprocal--8--on both sides.. |dw:1439343067959:dw|

34. anonymous

Multiply 8 on both sides. |dw:1439343171462:dw|

35. anonymous

From here, what do you think the answer will be? |dw:1439343201548:dw|

36. Jack1

if i could double medal u i would, awesome explanation @mathway

37. anonymous

i second Jack! im starting to completely understand!

38. anonymous

lol i'm flattered

39. anonymous

i have question though, what is the difference between the brackets and the parentheses?

40. anonymous

What do you mean? They are just the same, but not totally. I can't explain it.

41. anonymous

I was asking you a question btw @Abbs__ :D look at the drawing above

42. anonymous

f-1(x)=8(x+4)3

43. anonymous

Yes. :)

44. anonymous

You rock!