Thread: Finding features of the graph of a composite inverse tan function.

1. 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)]?

2. what do you want to study? domain? continuity? differentiability? integrability? huh?

3. i need all
domain
extremum
point of inflexion if there is
etc etc and finally
how to draw this curve

4. ahh well, those are straightforward stuff to make, so show what you've done.

5. infact i have alot of confusion
domain is ]-1,1[ for arccos
f'x=-(1+x^2)/2X
i think thats all

6. The domain of $\displaystyle f(x)=\arccos\left(\frac{1-x^2}{1+x^2}\right)$ consists of all values of $\displaystyle x$ such that

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

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

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

Inflection points are found where $\displaystyle f''(x)=0$, $\displaystyle f''(x)<0$ on one side next to the point, and $\displaystyle f''(x)>0$ on the other side next to the point.

7. thanks Scott H i understood

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