Q. The domain of the function $f(x) = \log_{2x - 1}{(x - 1)}$ is
A) $(1,\ \infty)$
B) $\left( \frac{1}{2},\ \infty \right)$
C) $(0,\ \infty)$
D) None of these
Explanation
(a)
For $f(x)$ to be defined
$x - 1 > 0$ and $2x - 1 > 0$ and $2x - 1 \neq 1$
$\Rightarrow x > 1,\ x > \frac{1}{2}$ and $x \neq 1$
$\Rightarrow x > 1$
Hence, domain is $(1,\ \infty)$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.