Question

The domain of the real valued function \[ f(x)=\cos^{-1}\!\left(\log_{5}\frac{x}{5}\right)+\log_{5}\!\left(\cos^{-1}\frac{x}{5}\right) \] is:

• A. \(\left[\frac15,5\right]\)
• B. \([1,25]\)
• C. \(\left(\frac15,1\right)\)
• D. \([1,5)\)

Hint:

For logarithmic functions, always ensure the argument is strictly positive. For inverse trigonometric functions, the input must lie in the allowed interval.

Answer 1

The Correct Option is D