Question

The interval where the function $\log (1+x)$ is continuous, is

• A. $(0,\infty )$
• B. $(-1,\infty )$
• C. $(-\infty ,-1)$
• D. None of the above

Answer 1

The correct option is B $(-1,\infty )$

$\because {\log }_{a}x$ is continuous where $x>0$ and $a>0,a\ne 1$, Therefore $\log (1+x)$ is continuous when $1+x>0$
$\Rightarrow x>-1$
$\therefore$ Required interval $=(-1,\infty )$