Q. Which of the following functions is one-to -one?
A) $f(x) = \sin{x,\ x \in \lbrack - \pi,\ \pi\rbrack}$
B) $f(x) = \sin{x,x \in \left\lbrack - \frac{3\pi}{2},\ - \frac{\pi}{4} \right\rbrack}$
C) $f(x) = \cos{x,\ x \in \left\lbrack - \frac{\pi}{2},\ \frac{\pi}{2} \right\rbrack}$
D) $f(x) = \cos{x,\ x \in \left\lbrack \pi,\ \frac{3\pi}{2} \right\rbrack}$
Explanation
(d)
[image:2_image8.emf]
[image:2_image9.emf]
In the given options (a), (b), (c), (e) the curves are decreasing and increasing in the given intervals, so it is not one-to-one function. But in option (d), the curve is only increasing in the given intervals, so it is one-to-one function.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.