Let f- R- R be defined by fx-x1-x2- x- R- Then the range of f is-

$i f f : R \to R i s d e f i n e d b y f (x) = \frac{s i n [x] π + t a n [x] π}{1 + [x^{2}]}, t h e n t h e r a n g e o f f = (w h e r e [x] d e n o t e s i n t e g r a l p a r t o f (x)$

Q. Let

f : R \to R

be a function defined by

f (x) = \frac{x^{2}}{x^{2} + 1}, \forall x \in R

. Find

f^{- 1}

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Let f:R→R be defined by f(x)=x1+x2, x∈R. Then the range of f is:

The correct option is B [−12,12]f(0)=0 & f(x) is odd.Further, if x>0 thenf(x)=1x+1x∈(0,12]Hence, f(x)∈[−12,12]

Let $f : R \to R$ be defined by $f (x) = \frac{x}{1 + x^{2}}$ , $x \in R$ . Then the range of f is:

The correct option is B $[- \frac{1}{2}, \frac{1}{2}]$
$f (0) = 0$ & $f (x)$ is odd.
Further, if $x > 0$ then
$f (x) = \frac{1}{x + \frac{1}{x}} \in (0, \frac{1}{2}]$
Hence, $f (x) \in [- \frac{1}{2}, \frac{1}{2}]$