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# c4 question Watch

1. 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...
2. (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.
3. (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'
4. (Original post by laurawoods)
hello i still don't understand why it cannot be 'equal to'
So, what value of x gives pi+1?
5. (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 and

so the domain does not contain and 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

where Arctanx is the main value of arctanx nad arctanx=Arctanx+k*\pi
So

and

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