QJEEM19Mad945: JEE Main 2019 Mathematics - Class 11 JEEM19Mad945 Solution: Let f : R → R be defined by f(x) = x 1 + x 2 , x ∈ R…

Question

Verified Solution • 2025–26 Session moderate

Let f : R

\to

R be defined by f(x) =

\frac{x}{1 + x^{2}}, x \in R

. Then the range of f is :

Accepted Answer

f(0) = 0 & f(x) is odd

Further, if x > 0 then

f(x) =

f (x) = \frac{1}{x + \frac{1}{x}} \in (0, \frac{1}{2}]

Hence,

f (x) \in [- \frac{1}{2}, \frac{1}{2}]

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