Q. Range of the function $f(x) = \frac{x^{2}}{x^{2} + 1}$ is
A) (-1, 0)
B) (-1, 1)
C) [0, 1)
D) (1, 1)
Explanation
(c)
Since, $f(x)$ is an even function therefore its values is always greater than equal to 0 and we know
$\ \ \ \ \ x^{2} < x^{2} + 1$ or $\frac{x^{2}}{x^{2} + 1} < 1$
$\therefore$ Required range is [0, 1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.