Let $f : R \to R$ defined by $f(x) = 2x^3 - 7$ for $x \in R$. Then :

(A) $f$ is one-one function

(B) $f$ is many to one function

(C) $f$ is bijective function

(D) $f$ is into function

Choose the correct answer from the options given below :

If $f\left(x+\dfrac{1}{x}\right) = x^2 + \dfrac{1}{x^2}$ then $f(x) =$

If $R$ is a relation on $Z$ (set of all integers) defined by $xRy$, iff $|x - y| \leq 1$, then

(a) $R$ is reflexive

(b) $R$ is symmetric

(c) $R$ is transitive

(d) $R$ is not symmetric

(e) $R$ is not transitive

Choose the most appropriate answer from the options given below

The domain of $y = \cos^{-1}(x^2 - 4)$ is

Let S be the set of all real numbers and let R be a relation on S, defined by $aRb \Leftrightarrow |a-b| \leq 1$. Then, R is

If $f(x) = \sqrt{x}$, $g(x) = 2x - 3$, then domain of $fog(x)$ 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