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anonymous

  • one year ago

I need help in finding the range of the following function: arcsin(3x+1) For finding the domain I did the following... -1 </= 3x + 1 </= 1 then I solved both sides of the inequality separately to get -2/3 </= x </= 0 Please correct me if I'm wrong :) *by "</=" I mean "less than or equal to".

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  1. Vocaloid
    • one year ago
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    yup, looks good to me! great job ~

  2. anonymous
    • one year ago
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    Great! Thanks @Vocaloid :) Ant ideas on how to find the range?

  3. anonymous
    • one year ago
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    Any*

  4. Vocaloid
    • one year ago
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    Hm, that's a bit trickier, I suppose you could evaluate arcsin(-2/3) and arcsin(0), but I'm sure there's a better way, let me think about this one for a second

  5. anonymous
    • one year ago
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    Alrighty! :D Thanks so much!

  6. anonymous
    • one year ago
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    I think the range of arcsin x is always -π/2 ≤ y ≤ π/2

  7. anonymous
    • one year ago
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    Wait would it be pi/2 - 3pi/2 ?

  8. jim_thompson5910
    • one year ago
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    I think you meant to say this for the domain \[\Large -1 \le 3x{\color{red}+}1 \le 1\] and you solve for x from there

  9. Vocaloid
    • one year ago
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    yes, peachpi is right, silly me!

  10. anonymous
    • one year ago
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    @jim_thompson5910 you caught my typo again >.<

  11. anonymous
    • one year ago
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    @peachpi thank you!

  12. jim_thompson5910
    • one year ago
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    but you have the correct result after you isolate x \[\Large -\frac{2}{3} \le x \le 0\] is the correct domain

  13. anonymous
    • one year ago
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    you're welcome

  14. anonymous
    • one year ago
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    @jim_thompson5910 okay so would be correct to find the range by just plugging in -2/3 and 0 ?

  15. anonymous
    • one year ago
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    *would it

  16. jim_thompson5910
    • one year ago
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    yep, plugging in x = -2/3 will give -pi/2 which is the lowest you can go in the range plugging in x = 0 will give pi/2 which is the highest you can go in the range

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