Question

Which one of the following statement is meaningless?

• A. ${\cos }^{-1}\left(ln\left(\frac{2e+4}{3}\right)\right)$
• B. $cose{c}^{-1}\left(\frac{\pi }{3}\right)$
• C. ${\cot }^{-1}\left(\frac{\pi }{2}\right)$
• D. ${\sec }^{-1}\left(\pi \right)$

Answer 1

The correct option is A ${\cos }^{-1}\left(ln\left(\frac{2e+4}{3}\right)\right)$

The domain for $f\left(x\right)=co{s}^{-1}\left(x\right)$ is $[-1,1]$

However, clearly $ln\left(\frac{2e+4}{3}\right)>1$

Since $f\left(x\right)$ for $|x|>1$ is not possible.

Option A is meaningless.