Questions: Find the exact value, if any, of the following composite function. Do not use a calculator. tan^(-1)(tan(10π/11)) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. tan^(-1)(tan(10π/11))= (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. It is not defined.

$Find the exact value, if any, of the following composite function. Do not use a calculator. tan^(-1)(tan(10π/11)) Select the correct choice below and, if necessary, fill in the answer box within your choice. A. tan^(-1)(tan(10π/11))= (Simplify your answer. Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.) B. It is not defined.$

Transcript text: Question 24, 7.1.47 of 30 points Points: 0 of 1 Save Find the exact value, if any, of the following composite function. Do not use a calculator. \[ \tan ^{-1}\left(\tan \frac{10 \pi}{11}\right) \] Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $\tan ^{-1}\left(\tan \frac{10 \pi}{11}\right)=$ $\square$ (Simplify your answer. Type an exact answer, using zas needed. Use integers or fractions for any numbers in the expression.) B. It is not defined.

Solution

Solution Steps

Step 1: Understanding the Problem

We are given the composite function tan(tan^{-1}(x)), where x is a real number. The goal is to find the exact value of this composite function.

Step 2: Applying the Solution Approach

For a trigonometric function followed by its inverse, such as tan(tan^{-1}(x)), the composite function simplifies to the argument of the inner function, which is x, provided x falls within the domain of the outer function. In this case, since we are dealing with tan(tan^{-1}(x)), and given that x is within the domain of the outer function (all real numbers), the solution simplifies to x.