List of top Mathematics Questions on Domain of a Function asked in CBSE Class XII

Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \] 

The domain of \[ f(x)=\cos^{-1}(2x-5) \] is: 

Find the domain of \[ p(x)=\sin^{-1}(1-2x^2). \] Hence, find the value(s) of \(x\) for which \[ p(x)=\frac{\pi}{6}. \] Also, write the range of \[ 2p(x)+\frac{\pi}{2}. \]
The domain of \( \sin^{-1}(1 - 2x) \) is :