analyze the function for domain, range, continuity, increasing or decreasing behavior; symmetry…

analyze the function for domain, range, continuity, increasing or decreasing behavior; symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=tan^(-1)x describe the symmetry of the function. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. symmetric with respect to the origin (odd) b. neither odd nor even, but symmetric with respect to the point (type an ordered pair. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) c. symmetric with respect to the origin (even) d. no symmetry the function is

analyze the function for domain, range, continuity, increasing or decreasing behavior; symmetry, boundedness, extrema, asymptotes, and end behavior. f(x)=tan^(-1)x describe the symmetry of the function. select the correct choice and, if necessary, fill in the answer box to complete your choice. a. symmetric with respect to the origin (odd) b. neither odd nor even, but symmetric with respect to the point (type an ordered pair. simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.) c. symmetric with respect to the origin (even) d. no symmetry the function is

Answer

Explanation:

Step1: Recall the property of odd - even functions

For a function (y = f(x)), if (f(-x)=-f(x)), it is odd; if (f(-x) = f(x)), it is even. Let (y = f(x)=\tan^{- 1}x). Then (f(-x)=\tan^{-1}(-x)). We know that (\tan^{-1}(-x)=-\tan^{-1}x) for all (x\in R).

Step2: Determine the symmetry type

Since (f(-x)=-\tan^{-1}x=-f(x)) for all (x\in(-\infty,\infty)), the function (y = \tan^{-1}x) is symmetric with respect to the origin, which means it is an odd - function.

Answer:

A. Symmetric with respect to the origin (odd)