VSA

Check whether $f:R-\{3\} \rightarrow R$ defined as $f(x)=\frac{x-2}{x-3}$ is onto or not.

SA

Let a relation $R$ in the set $R$ of real numbers be defined as $(a, b) \in R$ if and only if $1 + ab > 0$ for all $a, b \in R$. Check whether the relation $R$ is reflexive, symmetric or transitive.

LA

Show that a function $f : R \to R$ defined as $f(x) = \frac{5x - 3}{4}$ is both one-one and onto. [All India 2023]

MCQ_SINGLE

Let A={3,5}. Then number of reflexive relations on A is

SA

Is $g = \{(1, 1), (2, 3), (3, 5), (4, 7)\}$ a function? If this is described by the formula $g(x) = \alpha x + \beta$, then what values should be assigned to $\alpha$ and $\beta$? [Exemplar]

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