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KateNicole

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

  • 9 months ago
  • 9 months ago

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

    • 9 months ago
  2. KateNicole
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    \[f(x)=\sqrt[3]{\frac{ x }{ 8 }}-4\]

    • 9 months ago
  3. hartnn
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    oh, ok to get the inverse let y= f(x) and interchange 'x' and 'y'

    • 9 months ago
  4. timo86m
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    just solve for x and at the end swap x and y.

    • 9 months ago
  5. hartnn
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    \(y= \sqrt[3]{\dfrac{x}{8}}-4\\x= \sqrt[3]{\dfrac{y}{8}}-4\) solve for 'y' ! can you ?

    • 9 months ago
  6. timo86m
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    |dw:1372623159821:dw|

    • 9 months ago
  7. timo86m
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    maybe start with cuping both sides?

    • 9 months ago
  8. hartnn
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    ADD 4 and then cube both sides :)

    • 9 months ago
  9. timo86m
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    same thing :P

    • 9 months ago
  10. KateNicole
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    \[x ^{3}=\frac{ y }{ 8 } -4\]

    • 9 months ago
  11. hartnn
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    no, no.... we first would need to add 4 on both sides... first do that before cubing.

    • 9 months ago
  12. KateNicole
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    Oh...

    • 9 months ago
  13. timo86m
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    BUt adding 4 first will be easier :P

    • 9 months ago
  14. KateNicole
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    \[x+4=\sqrt[3]{\frac{ x }{ 8}}\]

    • 9 months ago
  15. KateNicole
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    \[x+4^{3}=\frac{ x }{ 8 } ?\]

    • 9 months ago
  16. timo86m
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    looks fishy.

    • 9 months ago
  17. hartnn
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    when you cube , you cube entirely, so it'll be (x+4)^3 = y/8 right ?

    • 9 months ago
  18. KateNicole
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    yea

    • 9 months ago
  19. hartnn
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    now what you can do to isolate 'y' ?

    • 9 months ago
  20. KateNicole
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    multiply by 8

    • 9 months ago
  21. hartnn
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    correct! do that and tell me what u get ?

    • 9 months ago
  22. KateNicole
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    (x+40)^3=y?

    • 9 months ago
  23. KateNicole
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    no, sorry

    • 9 months ago
  24. KateNicole
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    \[f ^{-1}(x)=8(x+4)^{3}\]

    • 9 months ago
  25. hartnn
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    correct! good :)

    • 9 months ago
  26. timo86m
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    remember do entirely. WHen you + / * square or cupe you do it to whole side.

    • 9 months ago
  27. timo86m
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    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.

    • 9 months ago
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