Question

The domain of the function \[ f(x)=\log_2\!\left(-\log_{\sqrt{2}}\!\left(1+\frac{1}{x^4}\right)-1\right) \] is:

• A. \((0,1)\)
• B. \((0,1]\)
• C. \([1,\infty)\)
• D. \((1,\infty)\)

Hint:

Always ensure arguments of logarithms are positive.

Answer 1

The Correct Option is D

Step 1: Argument of outer log must be positive.
Step 2: Solve inner logarithmic inequality to get \(x > 1\).