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    Just one question to ask you; please can you have a look at this question: Question 7 part i )

    http://www.mei.org.uk/files/papers/2011_Jan_c3.pdf

    I don't really understand how the range is –pi + 1 < f(x) < pi + 1

    I did get the same but i got less than or equal to and greater than or equal to .....? why is this not right because for the graph of arctan x the range includes greater than or equal to etc...
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    (Original post by laurawoods)
    Just one question to ask you; please can you have a look at this question: Question 7 part i )

    http://www.mei.org.uk/files/papers/2011_Jan_c3.pdf

    I don't really understand how the range is –pi + 1 < f(x) < pi + 1

    I did get the same but i got less than or equal to and greater than or equal to .....? why is this not right
    What real value of x gives pi+1? That's a trick question. And that's why it's the strict inequality.

    because for the graph of arctan x the range includes greater than or equal to etc...
    Don't know what particular document you're refering to there.
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    (Original post by ghostwalker)
    What real value of x gives pi+1? That's a trick question. And that's why it's the strict inequality.



    Don't know what particular document you're refering to there.
    hello i still don't understand why it cannot be 'equal to'
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    (Original post by laurawoods)
    hello i still don't understand why it cannot be 'equal to'
    So, what value of x gives pi+1?
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    (Original post by laurawoods)
    hello i still don't understand why it cannot be 'equal to'
    Because this function is originated from the tan(x) as inverse, adding some transformation to that (scalar multiplication by 2 and adding +1)

    THe tan(x) has vertical asymptote at -\frac{\pi}{2}+k\pi and
    \frac{\pi}{2}+k\pi
    so the domain does not contain \frac{-\pi}{2} and \frac{\pi}{2} for k=0 value (tanx tends to infinty there)
    From this follows the range of inverse arctan(x) does not contain these values, that is
    \frac{-\pi}{2}&lt;Arctan (x)&lt;\frac{\pi}{2}
    where Arctanx is the main value of arctanx nad arctanx=Arctanx+k*\pi
    So
    -\pi&lt;2\cdot Arctanx&lt; \pi
    and
    -\pi+1&lt;2Arctan(x)+1&lt;\pi+1
 
 
 
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