Category : JEE Main & Advanced
Function | Domain (D) | Range (R) |
\[{{\sin }^{-1}}x\] | \[-1\le x\le 1\] or \[[-1,\,1]\,\] | \[-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}\] or \[\left[ -\frac{\pi }{2},\,\frac{\pi }{2} \right]\] |
\[{{\cos }^{-1}}x\] | \[-1\le x\le 1\] or \[[-1,\,1]\] | \[0\le \theta \le \pi \]or \[[0,\,\pi ]\] |
\[{{\tan }^{-1}}x\] | \[-\infty <x<\infty \] i.e., \[x\in R\] or \[(-\infty ,\,\infty )\] | \[-\frac{\pi }{2}<\theta <\frac{\pi }{2}\] or \[\left( -\frac{\pi }{2},\,\frac{\pi }{2} \right)\] |
\[{{\cot }^{-1}}x\] | \[-\infty <x<\infty \] i.e., \[x\in R\] or \[(-\infty ,\,\infty )\] | \[0<\theta <\pi \] or \[(0,\,\pi )\] |
\[{{\sec }^{-1}}x\] | \[x\le -1,\,x\ge 1\] or \[(-\infty ,\,-1]\cup \,[1,\,\infty )\] | \[\theta \ne \frac{\pi }{2},\,0\le \theta \le \pi \] or \[\left[ 0,\,\frac{\pi }{2} \right)\,\cup \left( \frac{\pi }{2},\,\pi \right]\] |
\[\text{cose}{{\text{c}}^{-1}}x\] | \[x\le -1,\,x\ge 1\] or \[(-\infty ,\,-1]\,\cup \,[1,\,\infty )\] | \[\theta \ne 0,\,-\frac{\pi }{2}\le \theta \le \frac{\pi }{2}\] or \[\left[ -\frac{\pi }{2},\,0 \right)\,\cup \left( 0,\,\frac{\pi }{2} \right]\] |
You need to login to perform this action.
You will be redirected in
3 sec