The function $f: \mathrm{X} \rightarrow \mathrm{Y}$ defined by $f(\mathrm{x})=\cos \mathrm{x}$, where $\mathrm{x} \in \mathrm{X}$, is one-one and onto if X and Y are respectively equal to

• Correct answer
  A

  $[0, \pi]$ and $[-1,1]$
• B

  $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \operatorname{and}[-1,1]$
• C

  $[0, \pi]$ and $(-1,1)$
• D

  $[0, \pi]$ and $[0,1]$

Solution

Observe the cosx graph in the figure.
It is clear that, function is one - one and onto when x and y are $[0, \pi]$ and $[-1,1]$

Hence, the correct answer is option: 'A'.