SA

Prove that the function $f : R \to R$ given by $f(x) = x^3$ is bijective.

VSA

Let $f : R \to R$ be defined as $f(x) = \frac{x^2 + 1}{2}$, then check whether $f$ is one-one or onto.

VSA

If $A = \left\{x : -\frac{2}{5} \le x \le \frac{\pi - 2}{5}\right\}, B = \{y : -1 \le y \le 1\}$ and $f(x) = \cos(5x + 2)$, then the mapping $f : A \to B$ is

SA

Prove that the greatest integer function $f : R \to R$ given by $f(x) = [x]$, is neither one-one nor onto, where $[x]$ denotes the greatest integer less than or equal to $x$. [Competency]

LA

Prove that a function $f : [0, \infty) \to [-5, \infty)$ defined as $f(x) = 4x^2 + 4x - 5$ is both one-one and onto.

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