## anonymous one year ago Will METAL!! Find the inverse of the function. f(x) = the cube root of quantity x divided by seven. - 9 f-1(x) = 21(x + 9) f-1(x) = [7(x + 9)]3 f-1(x) = 7(x3 + 9) f-1(x) = 7(x + 9)3

1. anonymous

|dw:1443800798823:dw|

2. Nnesha

f(x) is same as y so first replace f(x) with y $\huge\rm \color{ReD}{y}=\sqrt[3]{\frac{\color{blue}{ x} }{ 7} } -9$ to find inverse switch x and y then solve for y

3. welshfella

isolate the cube root and cube both sides of the equation

4. anonymous

so how would I do that @Nnesha

5. Nnesha

switch x and y replace x with y and y with x

6. anonymous

|dw:1443801089795:dw|

7. Nnesha

looks good now first move -9 to the left and then take cube both sides to cancel out the cube root

8. anonymous

x + 9 |dw:1443801233219:dw|

9. anonymous

$\checkmark$

10. anonymous

what do I do know?

11. anonymous

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @Nnesha looks good now first move -9 to the left and then take cube both sides to cancel out the cube root $$\color{#0cbb34}{\text{End of Quote}}$$

12. Nnesha

take cube both sides to cancel out the cube root just like we take square to cancel out the square root $\large\rm \sqrt[4]{x} = (\sqrt[4]{x})^4 = (x^\frac{ 1 }{ \cancel{4} })^\cancel{4}=x$example

13. Nnesha

cube not cube root to cancel out the cube then we should take cube root

14. Nnesha

look at the example above^

15. anonymous

|dw:1443801529555:dw|

16. Nnesha

yes right but we should take cube both  sides |dw:1443801794531:dw| what would be the next step ?

17. anonymous

would it be x+3

18. Nnesha

to get rid of the fraction at right side what would you do ?

19. Nnesha

x+3 ?

20. anonymous

Idk would you move y to the other side.

21. Nnesha

we need y itself at right side so move 7 to the left side

22. Nnesha

7**

23. anonymous

|dw:1443802394930:dw|

24. Nnesha

-7 ??

25. Nnesha

is that a negative sign ?

26. anonymous

|dw:1443802476561:dw|

27. Nnesha

to cancel out the 7 at right side we should multiply both sides by 7|dw:1443802496552:dw| that's how it's 7 times (x+9)^3

28. Nnesha

it's (x+9)^3 like i said we should take cube both sides

29. anonymous

Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 14)2 - 9 Shift the graph of y = x2 right 14 units and then up 9 units. Shift the graph of y = x2 down 14 units and then left 9 units. Shift the graph of y = x2 right 14 units and then down 9 units. Shift the graph of y = x2 left 14 units and then down 9 units.

30. anonymous

Do you have a graphing calculator? @Nnesha

31. Nnesha

f(x-h)= horizontal shift ( if h is negative shift some units to the right , if h is positive shift h units to the left ) f(x) + k =vertical shift ( positive k shift up , if k is negative shift k units down)

32. Nnesha

yes

33. anonymous

So would it be answer choice the last one then right?

34. Nnesha

you don't need calculator for this question .

35. anonymous

y = (x - 14)2 - 9 because -9 is and (x-14)^2 is negative as well.

36. anonymous

*negative

37. Nnesha

no h =-14 so read what i said above

38. anonymous

oh ok so it's our third option.

39. Nnesha

right if h is negative then shift right if it's positive then left shift