Question

the domain and range of function log(|logx|) is​

Answer 1

function f(x)= log x

domain=(0,infinity)

note->if g(x) is a function and it is the inverse of a function f(x) the range of f(x)=domain of g(x)

since log x is the inverse function of exponential function a^x where a>0 and x is real number

as it is clear range of exponential function a^x is (0,infinity)

so domain of log x =(0,infinity)

Answer 2

Answer:

The domain and range of $f(x)= log(|log x|)$ are $(0, \infty)$ and $(-\infty,\infty)$ respectively.

Step-by-step explanation:

Given the function $f(x)= log(|log x|)$

The given expression is defined only when $x > 0$.

And also the argument of the external logarithm, which is $logx$ also has to be greater than 0.

$\implies logx > 0$

$\implies x > 10^{o} =1$

and hence both the conditions $x > 0$ and $x > 1$ must be true.

The domain of a function is all values of x that make the expression defined.

Therefore, the domain of the given function is $(0, \infty)$

which can also be written as $x\in(0,1)\cup(0,\infty)$

The range of the function is the set of all possible f(x) values.

As $x$ approaches, $f(x)$ approaches infinity.

And the range of f(x) is $(-\infty,\infty)$.

Therefore, the domain and range of $f(x)= log(|log x|)$ are $(0, \infty)$ and $(-\infty,\infty)$ respectively.