Consider a function $f:[-1,1] \to Y$ defined as $f(x)=\dfrac{x}{x+2}$ and $Y=range(f(x))$, then which of following statements are correct?

(A) Function $f(x)$ is one-one

(B) Function $f(x)$ is not one-one

(C) Function $f(x)$ is onto

(D) Function $f(x)$ is invertible

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If $f: R \to R$ is defined by $f(x) = \sin x + x$, then $f(f(x))$ is:

Given the relation $R=\{(1,2),(2,3)\}$ on a set $A=\{1,2,3\}$, then which of following statements are TRUE?

A. Minimum number of ordered pairs are added to R so that enlarged relation is reflexive is 3

B. Minimum number of ordered pairs are added to R so that enlarged relation is symmetric is 2

C. Minimum number of ordered pairs are added to R so that enlarged relation is an equivalence relation is 7

D. Minimum number of ordered pair are added to R so that enlarged relation is an equivalence relation is 6.

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The graph given below represents which of the following function?

Let $A = \{a, b, c\}$. Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

If $n(A) = 3$, $n(B) = 2$, then number of all possible surjective function from set A to set B are :

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = [x]$, where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?

(A) f is one-one but not onto

(B) f is not onto

(C) f is not one-one

(D) f is one-one and onto

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