Chapter 6.8, Problem 34E

To determine

To state: true or false, and give a counterexample in case of false statement.

Answer to Problem 34E

False

Explanation of Solution

Given information:

  $\text{Arccos }x=\text{Arccos }\left(-x\right)\text{ for }-1\le x\le 1$

Calculation:

Let $x=-1$ and put the value in the given relation and solve as follows:

  $\begin{array}{c}\text{Arccos }\left(x\right)=\text{Arccos }\left(-x\right)\\ \text{Arccos }\left(-1\right)=\text{Arccos }\left(-\left(-1\right)\right)\\ \pi =0\\ LHS\ne RHS\end{array}$

Thus, the definition for given relation is false.