anonymous 2 years ago Find the inverse of the function. f(x) = cube root x/8 -4

1. hartnn

is that $$f(x)=(\sqrt[3]x/8) -4$$ ?

2. anonymous

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

3. hartnn

oh, ok to get the inverse let y= f(x) and interchange 'x' and 'y'

4. anonymous

just solve for x and at the end swap x and y.

5. hartnn

$$y= \sqrt[3]{\dfrac{x}{8}}-4\\x= \sqrt[3]{\dfrac{y}{8}}-4$$ solve for 'y' ! can you ?

6. anonymous

|dw:1372623159821:dw|

7. anonymous

8. hartnn

ADD 4 and then cube both sides :)

9. anonymous

same thing :P

10. anonymous

$x ^{3}=\frac{ y }{ 8 } -4$

11. hartnn

no, no.... we first would need to add 4 on both sides... first do that before cubing.

12. anonymous

Oh...

13. anonymous

BUt adding 4 first will be easier :P

14. anonymous

$x+4=\sqrt[3]{\frac{ x }{ 8}}$

15. anonymous

$x+4^{3}=\frac{ x }{ 8 } ?$

16. anonymous

looks fishy.

17. hartnn

when you cube , you cube entirely, so it'll be (x+4)^3 = y/8 right ?

18. anonymous

yea

19. hartnn

now what you can do to isolate 'y' ?

20. anonymous

multiply by 8

21. hartnn

correct! do that and tell me what u get ?

22. anonymous

(x+40)^3=y?

23. anonymous

no, sorry

24. anonymous

$f ^{-1}(x)=8(x+4)^{3}$

25. hartnn

correct! good :)

26. anonymous

remember do entirely. WHen you + / * square or cupe you do it to whole side.

27. anonymous

1 tip use parenthesis a+b=c+d if they tell you divide both sides by t a+b=c+d (a+b)/t=(c+d)/t use perenthesis cuzz that says do it to whole thing --- another tip If told to square both sides a+b=c+d (a+b)^2=(c+d)^2 but (a+b)^2=(c+d)^2 is not a^2+b^2=c^2+d^2 it is (a+b)*(a*b)=(c+d)*(c+d) Maybe you knew but lots of people assume or forget.

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