1
JEE Main 2017 (Offline)
+4
-1
The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as

$$f\left( x \right) = {x \over {1 + {x^2}}}$$, is
A
invertible
B
injective but not surjective.
C
surjective but not injective
D
neither injective nor surjective.
2
JEE Main 2017 (Offline)
+4
-1
Let $$a$$, b, c $$\in R$$. If $$f$$(x) = ax2 + bx + c is such that
$$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$$(y) + xy, $$\forall x,y \in R,$$

then $$\sum\limits_{n = 1}^{10} {f(n)}$$ is equal to
A
165
B
190
C
255
D
330
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
For x $$\in$$ R, x $$\ne$$ 0, Let f0(x) = $${1 \over {1 - x}}$$ and
fn+1 (x) = f0(fn(x)), n = 0, 1, 2, . . . .

Then the value of f100(3) + f1$$\left( {{2 \over 3}} \right)$$ + f2$$\left( {{3 \over 2}} \right)$$ is equal to :
A
$${8 \over 3}$$
B
$${5 \over 3}$$
C
$${4 \over 3}$$
D
$${1 \over 3}$$
4
JEE Main 2016 (Offline)
+4
-1
If $f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0$, and $\mathrm{S}=\{x \in \mathbf{R}: f(x)=f(-x)\}$; then $\mathrm{S}:$
A
is an empty set.
B
contains exactly one element.
C
contains exactly two elements.
D
contains more than two elements.
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