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osanseviero

  • 2 years ago

The domain of a composition of two functions

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

  2. hartnn
    • 2 years ago
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    what did you get for f(g(x)) = .... ?

  3. osanseviero
    • 2 years ago
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    Let me do it, give me a sec

  4. hartnn
    • 2 years ago
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    sure, take your time :)

  5. osanseviero
    • 2 years ago
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    \[\sqrt{2-4x}\]

  6. osanseviero
    • 2 years ago
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    ooops sorry, confused question, give me another sec

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

  8. osanseviero
    • 2 years ago
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    Sorry, the mistake was the question

  9. osanseviero
    • 2 years ago
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    \[f(x)=\sqrt{x+1}\] g(x)=1-4x

  10. hartnn
    • 2 years ago
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    yes, f(g(x)) is correct then

  11. hartnn
    • 2 years ago
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    now quantity under square root cannot be negative

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

  13. osanseviero
    • 2 years ago
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    [-1,1/2]

  14. hartnn
    • 2 years ago
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    yep, thats correct! good :)

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

  16. osanseviero
    • 2 years ago
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    And intersect that with the domain of the last result?

  17. hartnn
    • 2 years ago
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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

  18. osanseviero
    • 2 years ago
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    Perfect, thanks

  19. hartnn
    • 2 years ago
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    welcome ^_^

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