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Math Help - Finding features of the graph of a composite inverse tan function.

  1. #1
    ali
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    Finding features of the graph of a composite inverse tan function.

    study a function defined by f(x)=Arccos[(1-x^2)/(1+x^2)]?
    Last edited by mr fantastic; October 19th 2009 at 03:01 PM. Reason: Changed post title
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  2. #2
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    what do you want to study? domain? continuity? differentiability? integrability? huh?
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  3. #3
    ali
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    i need all
    domain
    extremum
    point of inflexion if there is
    etc etc and finally
    how to draw this curve
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  4. #4
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    ahh well, those are straightforward stuff to make, so show what you've done.
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  5. #5
    ali
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    infact i have alot of confusion
    domain is ]-1,1[ for arccos
    f'x=-(1+x^2)/2X
    i think thats all
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  6. #6
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    The domain of f(x)=\arccos\left(\frac{1-x^2}{1+x^2}\right) consists of all values of x such that

    -1\le \frac{1-x^2}{1+x^2}\le 1.

    I found a different answer for both the domain and f'(x). Hint: since 1+x^2 is positive, multiplying the three expressions by 1+x^2 will preserve the inequalities and result in an equivalent statement.

    Extrema are found only at critical points, i.e., boundary points, points at which f'(x)=0, and points at which f'(x) doesn't exist.

    Inflection points are found where f''(x)=0, f''(x)<0 on one side next to the point, and f''(x)>0 on the other side next to the point.
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  7. #7
    ali
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    thanks Scott H i understood
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