Question

$f:(-\frac{\pi }{2},\frac{\pi }{2})\to (\infty ,\infty ),f\left(x\right)=\tan x$ is.

• A. one-one and onto
• B. one-one but not onto
• C. onto but not one-one
• D. neither one-one nor onto

Answer 1

The correct option is A one-one and onto

$f^{\prime }\left(x\right)={\sec }^{2}x>0$
Therefore, $f$ is increasing in $(-\frac{\pi }{2},\frac{\pi }{2})\Rightarrow f$ is one one
and range of $f$ in $(-\frac{\pi }{2},\frac{\pi }{2})$ is $(-\infty ,\infty )$
Therefore, $f$ is onto