If a function $f: R \to T$, defined by $f(x) = \sqrt{3}\sin x + \cos x$ is an onto function, then the interval of $T$ is

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

Choose the correct answer from the options given below:

If R is a relation on $A = \{a, b, c\}$ such that $R = \{(a,a), (b,b)\}$, which element/elements should be included to make R an equivalence relation.

A. (c, c)

B. (c, c), (a, c), (c, a)

C. (a, b), (b, c), (a, c)

D. (b, c), (c, c), (c, a), (b, a)

Choose the correct answer from the options given below:

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) = \frac{x}{x^2+1}$ then

The function $f: R \to [0,1]$ defined by $f(x) = \dfrac{x^2}{x^2+1}$ is: (Where $R$ is set of real numbers)

A. One-one

B. one-one and onto

C. onto

D. Not one-one

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

Let $f: \mathbb{R} \to \mathbb{R}$ be defined as $f(x) = 100x + 1$, where $\mathbb{R}$ is a set of real numbers, then