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osanseviero Group Title

The domain of a composition of two functions

  • one year ago
  • one year ago

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  1. osanseviero Group Title
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    Natural domain of \[f(x)=\frac{ 1 }{ x-3 }\] g(x)=5x \[(Fog)(x)\] It is x\[x \in[-1,infinite)\] ?

    • one year ago
  2. hartnn Group Title
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    what did you get for f(g(x)) = .... ?

    • one year ago
  3. osanseviero Group Title
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    Let me do it, give me a sec

    • one year ago
  4. hartnn Group Title
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    sure, take your time :)

    • one year ago
  5. osanseviero Group Title
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    \[\sqrt{2-4x}\]

    • one year ago
  6. osanseviero Group Title
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    ooops sorry, confused question, give me another sec

    • one year ago
  7. hartnn Group Title
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    am i reading the question correct ? f(x) =1/ (x-3) g(x) =5x ? i don't see ..... oh, okk

    • one year ago
  8. osanseviero Group Title
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    Sorry, the mistake was the question

    • one year ago
  9. osanseviero Group Title
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    \[f(x)=\sqrt{x+1}\] g(x)=1-4x

    • one year ago
  10. hartnn Group Title
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    yes, f(g(x)) is correct then

    • one year ago
  11. hartnn Group Title
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    now quantity under square root cannot be negative

    • one year ago
  12. osanseviero Group Title
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    So the domain is x<= 1/2 for the square root, and I take the intersection

    • one year ago
  13. osanseviero Group Title
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    [-1,1/2]

    • one year ago
  14. hartnn Group Title
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    yep, thats correct! good :)

    • one year ago
  15. osanseviero Group Title
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    So I need to take the domain of FoG with \[\left\{ x \in Dg|g(x)\in Df \right\}\]

    • one year ago
  16. osanseviero Group Title
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    And intersect that with the domain of the last result?

    • one year ago
  17. hartnn Group Title
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    i am not sure about what that notation says, but yes, you take the intersection domains of both the funtion with composite function to get the final domain

    • one year ago
  18. osanseviero Group Title
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    Perfect, thanks

    • one year ago
  19. hartnn Group Title
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    welcome ^_^

    • one year ago
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