Question

Secant function is bijective when its domain and range are ..A.. and $R-(-1,1)$ respectively. Here A refers to

• A. $[0,\pi ]$
• B. $\left[0,\frac{\pi }{2}\right]$
• C. $[0,\pi ]-\left\{\frac{\pi }{2}\right\}$
• D. None of these

Answer 1

Answer: (C)

If we restrict the domain of secant function to $[0,\pi ]-\left\{\frac{\pi }{2}\right\}$, then it is one-one and onto with its range as the set $R-(-1,1)$. Actually, secant function restricted to any of the intervals $[-\pi ,0]-\left\{\frac{-\pi }{2}\right\},[0,\pi ]-\left\{\frac{\pi }{2}\right\},[\pi ,2\pi ]-\left\{\frac{3\pi }{2}\right\}$ etc., is bijective and its range is $R-(-1,1)$.