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(i) $f(x)=3x-2$ where $f: \mathbb{R}\rightarrow \mathbb{R}$ # Method 1: Let $x_1, \; x_2$ be any element of $\mathbb{…

Given:   $\hspace{0.3cm}A=\mathbb{R}-\{3\}$ $\hspace{0.3cm}B=\mathbb{R}-\{1\}$ $\hspace{0.3cm}f:A\rightarrow B$ s…

Numbers which have atleast one factor other than $𝟏$ and the number itself are called composite numbers. Example: $4…

Fundamental Theorem of Arithmetic (FTA) states that every composite number can be uniquely expressed as a product of pr…

Given: $\sqrt{3}$ is irrational. To Prove: $5+2\sqrt{3}$ is irrational. Proof: Suppose that $5+2\sqrt{3}$ is a ration…