LA

Show that the function $f : R \to \{x \in R : -1 < x < 1\}$ defined by $f(x) = \frac{x}{1 + |x|}, x \in R$ is one-one and onto function.

MCQ_SINGLE

A function \(f:\mathbb{R}\rightarrow\mathbb{R}\) defined as \(f(x)=x^{2}-4x+5\) is:

SA

Prove that the function $f$ is surjective, where $f : N \to N$ such that $f(n) = \begin{cases} \frac{n + 1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$.

LA

Show that a function $f : N \to N$ be defined by $f(n) = \begin{cases} 2n, & n = 2, 4, 6, 8, \dots \\ n - 1, & n = 3, 7, 11, 15, \dots \\ \frac{n + 1}{2}, & n = 1, 5, 9, 13, \dots \end{cases}$ then $f$ is bijective. [Competency]

VSA

Check whether $f:Z\times Z \rightarrow Z\times Z$ (where Z is the set of integers) defined as $f(x,y)=(2y,3x)$ is injective or not.

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