Question

If a real valued function \(f:A\rightarrow B\) defined by \[ f(x)=\sin^{-1}\!\left(\sqrt{x^{2}-4x+5}\right) \] is a bijection, then \(A\cup B=\)

• A. \(\mathbb R\)
• B. \([0,1]\cup\left[0,\frac{\pi}{2}\right]\)
• C. \([-1,1]\cup\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)
• D. \(\left\{2,\frac{\pi}{2}\right\}\) \bigskip

Hint:

Whenever an inverse trigonometric function appears, first check whether its argument lies in the permitted interval. Most questions become simple after applying this restriction.

Answer 1

The Correct Option is D