Domain of f(x)= | x| is - Vidyadip

MCQ

Domain of $f(x)=\log |\log x|$ is

A
$(0, \infty)$
B
$(1, \infty)$
✓
$(0,1) \cup(1, \infty)$
D
$(-\infty, 1)$

✓

Answer

Correct option: C.

$(0,1) \cup(1, \infty)$

(C)
$f (x)=\log |\log x|, f (x)$ is defined if $|\log x|>0$ and $x>0$, i.e., if $x>0$ and $x \neq 1$
$\ldots[\because |\log x|>0$ if $x \neq 1]$
$\Rightarrow x \in(0,1) \cup(1, \infty)$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Functions→Functions — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\lim _{x \rightarrow 0} \frac{2^x-1}{(1+x)^{1 / 2}-1}=$

If $f(x)=\left\{\begin{array}{c}\frac{\sin [x]}{[x]+1}, \text { for } x>0 \\ \frac{\cos \frac{\pi}{2}[x]}{[x]}, \text { for } x<0 ; \\ k, \text { for } x=0\end{array}\right.$
where $[x]$ denotes the greatest integer less than or equal to $x$, then in order that f be continuous at $x=0$, the value of k is

The directrix of the parabola $x^2 - 4x - 8y + 12 = 0$ is

The common ratio for the G.P. 0.12, 0.24, 0.48, is

$\cot\left(45^{\circ}+\theta\right)\cot\left(45^{\circ}-\theta\right)=$

The value of $\lim _{x \rightarrow 0} \frac{27^x-9^x-3^x+1}{\sqrt{5}-\sqrt{4+\cos x}}$ is

The value of $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \frac{11 \pi}{14} \sin \frac{13 \pi}{14}$ is

The equations of tangents to the circle $x^2+y^2-22 x-4 y+25=0$ which are perpendicular to the line $5 x+12 y+8=0$ are

If both mean and variance of $50$ observations $x_1, x_2, \ldots . ., x_{50}$ are equal to $16$ and $256$ respectively, then mean of $\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots,\left(x_{50}-5\right)^2$ is

The value of $\cos 52^{\circ}+\cos 68^{\circ}+\cos 172^{\circ}$ is