Question

The sum of all the integers in the domain of the real valued function \[ f(x)=\sqrt{\log_{\frac13}\left(\frac{9x-30}{x-26}\right)} \]

• A. 6
• B. 9
• C. 12
• D. 10

Hint:

For \[ \sqrt{\log_a(f(x))} \] always use \[ \log_a(f(x))\ge0. \] If \[ 0<a<1, \] then \[ \boxed{\log_a t\ge0 \iff 0<t\le1.} \] If \[ a>1, \] then \[ \boxed{\log_a t\ge0 \iff t\ge1.} \]

Answer 1

The Correct Option is A