LA

Let $A = R - \{5\}$ and $B = R - \{1\}$. Consider the function $f : A \to B$, defined by $f(x) = \frac{x - 3}{x - 5}$. Show that $f$ is one - one and onto. [All India 2024]

LA

Show that a function $f : R \to R$ defined by $f(x) = \frac{2x}{1 + x^2}$ is neither one-one nor onto. Further, find set $A$ so that the given function $f : R \to A$ becomes an onto function. [All India 2023, Delhi 2024]

LA

Let $f : R \to R$ be a function defined by $f(x) = x^3 + 4$, then show that $f$ is bijective.

MCQ_SINGLE

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

LA

Let $f : R - \left\{-\frac{4}{3}\right\} \to R$ be a function defined as $f(x) = \frac{4x}{3x + 4}$. Show that $f$ is one -one function. Also, check whether $f$ is an onto function or not. [All India 2017, All India 2023]

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