Question

Which of the following functions in the interval's mentioned are one-one functions.

• A. $\sin x,x\in (0,2\pi )$
• B. $\sin x,x\in (\frac{\pi }{2},\frac{3\pi }{2})$
• C. $\tan x,x\in (0,\pi )-\left\{\frac{\pi }{2}\right\}$
• D. $\tan x,x\in (\frac{\pi }{2},\frac{3\pi }{2})$

Answer 1

Answer: (B), (C), (D)

$\tan x,x\in (\frac{\pi }{2},\frac{3\pi }{2})$

Graph of $\sin x:$


Graph of $\tan x:$


Clearly, from the above given graphs, using horizontal line test, we can say that $\sin x$ in $(\frac{\pi }{2},\frac{3\pi }{2})$ and $\tan x$ in $(0,\pi )-\left\{\frac{\pi }{2}\right\}$ as well as in $(\frac{\pi }{2},\frac{3\pi }{2})$ are one-one functions.