Question

$f :(0, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ 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)

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