Question

$f:(0,\infty )\to \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ be defined as, $f(x)=\arctan (\ell nx)$
The above function can be classified as

• A. injective but not surjective
• B. surjective but not injective
• C. neither injective nor surjective
• D. both injective as well as surjective

Answer 1

Answer: (D)

$f(x)={\tan }^{-1}(\ln x)$
$\because {\tan }^{-1}(x)\&\ell nx$ are increasing functions.
$\Rightarrow f(x)$ is also increasing function.