LA

Let $R$ be relation defined on the set of natural number $N$ as follows, $R = \{(x, y) : x \in N, y \in N, 2x + y = 41\}$. Find the domain and range of the relation $R$. Also verify whether $R$ is reflexive, symmetric and transitive. [Exemplar]

SA

Check whether the relation $R$ in $R$ defined by $R = \{(a, b) : a \le b^3\}$ is reflexive, symmetric or transitive. [All India 2024]

LA

Show that the function $f : R_* \to R_*$ defined by $f(x) = \frac{1}{x}$ is one-one onto, where $R_*$ is the set of all non-zero real numbers. Is the result true, if the domain $R_*$ is replaced by $N$ with co-domain being same as $R_*$?

LA

A function $f : \mathbb{R} - \left\{\frac{3}{5}\right\} \longrightarrow \mathbb{R} - \left\{\frac{3}{5}\right\}$ is defined as $f(x) = \frac{3x + 2}{5x - 3}$. Show that f is one-one and onto.

SA

Let $D$ be the domain of the real valued function $f$ defined by $f(x) = \sqrt{25 - x^2}$. Then, write $D$.

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